ADVANCED PHYSICS COURSE CHAPTER 7: THERMODYNAMICS€¦ · CHAPTER 7: THERMODYNAMICS FOR HIGH SCHOOL PHYSICS CURRICULUM AND ALSO THE PREPARATION OF ACT, DSST, AND AP EXAMS This is

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A D V A N C E D P H Y S I C S C O U R S E

C H A P T E R 7 :

T H E R M O D Y N A M I C S

FOR HIGH SCHOOL PHYSICS CURRICULUM AND ALSO THE PREPARATION OF ACT, DSST, AND AP EXAMS

This is a complete video-based high school physics course that includes videos, labs, and hands-on learning. You

can use it as your core high school physics curriculum, or as a college-level test prep course. Either way, you’ll

find that this course will not only guide you through every step preparing for college and advanced placement

exams in the field of physics, but also give you in hands-on lab practice so you have a full and complete

education in physics. Includes text reading, exercises, lab worksheets, homework and answer keys.

BY AURORA LIPPER ∙ SUPERCHARGED SCIENCE 2017


TABLE OF CONTENTS

Material List .................................................................................................................................................................................................................... 3

introduction .................................................................................................................................................................................................................... 4

Thermal Physics Introduction ................................................................................................................................................................................. 5

Temperature ................................................................................................................................................................................................................... 6

Absolute Zero .................................................................................................................................................................................................................. 7

Thermometers ............................................................................................................................................................................................................... 8

Thermal Energy ............................................................................................................................................................................................................. 9

The Human Body ........................................................................................................................................................................................................ 10

Changing Molecular Speeds ................................................................................................................................................................................... 15

States of Matter ........................................................................................................................................................................................................... 16

Melting and Evaporation ........................................................................................................................................................................................ 20

Condensation and Freezing ................................................................................................................................................................................... 25

What are clouds? ........................................................................................................................................................................................................ 32

Changing States at Unusual Places ...................................................................................................................................................................... 33

Heat .................................................................................................................................................................................................................................. 34

Heat goes from hot to cold ..................................................................................................................................................................................... 35

Heat Capacity ............................................................................................................................................................................................................... 36

Specific Heat Capacity .............................................................................................................................................................................................. 37

Fire Water Balloon .................................................................................................................................................................................................... 38

How much energy does a candy bar have? ..................................................................................................................................................... 43

Heat Flow ...................................................................................................................................................................................................................... 44

Heat and States of Matter ....................................................................................................................................................................................... 45

Sublimation .................................................................................................................................................................................................................. 46

Heat Energy of a Peanut .......................................................................................................................................................................................... 47

Thermostat ................................................................................................................................................................................................................... 56

Triple Point ................................................................................................................................................................................................................... 57

Conduction .................................................................................................................................................................................................................... 58

Convection .................................................................................................................................................................................................................... 59

Convection Currents ................................................................................................................................................................................................. 60

Radiation ....................................................................................................................................................................................................................... 61

Calorimeter ................................................................................................................................................................................................................... 66

Heat Engines ................................................................................................................................................................................................................ 67

Hero Engine .................................................................................................................................................................................................................. 72

Stirling Engine ............................................................................................................................................................................................................. 73

Ideal Gas Law ............................................................................................................................................................................................................... 81

Homeowrk Problems with Solutions ................................................................................................................................................................. 83


MATERIAL LIST

While you can do the entire course entirely on paper, it’s not really recommended since physics is based in real-world observations and experiments! Here’s the list of materials you need in order to complete all the experiments in this unit. Please note: you do not have to do ALL the experiments in the course to have an outstanding science education.

Simply pick and choose the ones you have the interest, time and budget for.

alcohol burner or candle with adult help

balloons

black spray paint

bottles of water (2)

candles

CDs (3 old ones)

chemistry stand with glass test tube and

holder coin

drill with 1/16″ bit

electrical tape

electrical wire (3- conductor solid wire)

fire extinguisher

fishing line (15lb. test or similar)

foil wrapper (from stick of gum or candy bar)

food coloring

freezer

ice cubes

incandescent light (or sunlight)

index cards

matches or lighter (and adult help)

mug with hot water

nylon bushing (from hardware store)

old inner tube from a bike wheel

pack of steel wool

paper clip paper, one sheet of each: white and

black

penny

pepper

permanent marker

plastic bottle

plastic syringe

push pin

raw peanuts

razor

rubbing alcohol

scissors

silver highlighter (or aluminum foil)

silver or white spray paint

small pliers

soda bottle (2L)

soda can (4)

solar drinking bird

super glue and instant dry

Swiss army knife (with can opener option)

tape

thermal paper (“Liquid Crystal Sheet” – see

website for ordering information)

wire cutters


INTRODUCTION

If you put an ice cube in a glass of lemonade, the ice cube melts. The thermal energy from your lemonade moves to the ice cube. Increasing the temperature of the ice cube and decreasing the temperature of your lemonade. The movement of thermal energy is called heat. The ice cube receives heat from your lemonade. Your lemonade gives heat to the ice cube. Heat can only move from an object of higher temperature to an object of lower temperature. We’re going to learn about temperature, heat energy, atoms, matter, phase changes, and more in our unit on Thermodynamics as we build steam boats, fire-water balloons, hero engines, thermostats, Stirling engines, and more! Does this sound familiar? “I’m too cold. Get me a sweater!” “This soup’s too hot!” “Phew, I’m sweating.” “Yowtch, that pan handle burned me!” If you’ve ever made any of the above comments, then you were talking about thermal energy. Very clever of you, don’t you think? Thermal energy is basically the energy of the molecules moving inside something. The faster the molecules are moving, the more thermal energy that something has. The slower they are moving, the less thermal energy that something has. I’m sure at some point you’ve said, “Wow, my internal thermal energy is way high! I need a liquid with a low thermal energy.” What… you’ve never said that?! Oh, wait. I bet it sounded like this when you said it, “Wow, I’m hot! I need a cool drink.” Whenever we talk about the temperature of something we are talking about its thermal energy. Objects whose molecules are moving very quickly are said to have high thermal energy or high temperature. The higher the temperature, the faster the molecules are moving. You may remember that temperature is just a speedometer for molecules. You may have asked yourself the question, “So, if everything is made of molecules, and these molecules are often speeding up and slowing down…what happens to the stuff these molecules are are made of if they change speed a lot? Will my kitchen table start vibrating across the room if the table somehow gets too hot?” No, it’s pretty unlikely that your table will begin jumping around the room, no matter how hot it gets. However, some interesting things do happen when molecules change speeds.


THERMAL PHYSICS INTRODUCTION

Here’s a teleclass to get you started on learning about Thermodynamics. The next set of lessons will take you in more detail on each topic covered in the teleclass (and more)!


TEMPERATURE

Temperature is a way of talking about, measuring, and comparing the thermal energy of objects. We use three different kinds of scales to measure temperature. Fahrenheit, Celsius, and Kelvin. (The fourth, Rankine, which is the absolute scale for Fahrenheit, is the one you’ll learn about in college.) Mr. Fahrenheit, way back when (18th century) created a scale using a mercury thermometer to measure temperature. He marked 0° as the temperature ice melts in a tub of salt. (Ice melts at lower temperatures when it sits in salt. This is why we salt our driveways to get rid of ice). To standardize the higher point of his scale, he used the body temperature of his wife, 96°. As you can tell, this wasn’t the most precise or useful measuring device. I can just imagine Mr. Fahrenheit, “Hmmm, something cold…something cold. I got it! Ice in salt. Good, okay there’s zero, excellent. Now, for something hot. Ummm, my wife! She always feels warm. Perfect, 96°. ” I hope he never tried to make a thermometer when she had a fever. Just kidding, I’m sure he was very precise and careful, but it does seem kind of weird. Over time, the scale was made more precise and today body temperature is usually around 98.6°F. Later, (still 18th century) Mr. Celsius came along and created his scale. He decided that he was going to use water as his standard. He chose the temperature that water freezes at as his 0° mark. He chose the temperature that water boils at as his 100° mark. From there, he put in 100 evenly spaced lines and a thermometer was born. Last but not least Mr. Kelvin came along and wanted to create another scale. He said, I want my zero to be ZERO! So he chose absolute zero to be the zero on his scale.


ABSOLUTE ZERO

Absolute zero is the theoretical temperature where molecules and atoms stop moving. They do not vibrate, jiggle or anything at absolute zero. In Celsius, absolute zero is -273 ° C. In Fahrenheit, absolute zero is -459°F (or 0°R). It doesn’t get colder than that!


THERMOMETERS

As you can see, creating the temperature scales was really rather arbitrary: “I think 0° is when water freezes with salt.” “I think it’s just when water freezes.” “Oh, yea, well I think it’s when atoms stop!” Many of our measuring systems started rather arbitrarily and then, due to standardization over time, became the systems we use today. So that’s how temperature is measured, but what is temperature measuring?


THERMAL ENERGY

Temperature is measuring thermal energy which is how fast the molecules in something are vibrating and moving. The higher the temperature something has, the faster the molecules are moving. Water at 34°F has molecules moving much more slowly than water at 150°F. Temperature is really a molecular speedometer. When something feels hot to you, the molecules in that something are moving very fast. When something feels cool to you, the molecules in that object aren’t moving quite so fast.


THE HUMAN BODY

Believe it or not, your body perceives how fast molecules are moving by how hot or cold something feels. Your body has a variety of antennae to detect energy. Your eyes perceive certain frequencies of electromagnetic waves as light. Your ears perceive certain frequencies of longitudinal waves as sound. Your skin, mouth and tongue can perceive thermal energy as hot or cold. What a magnificent energy sensing instrument you are! Let’s test this out now with three different cups of water (I colored mine in the video so you could tell which is which): Objects whose molecules are moving very quickly are said to have high thermal energy or high temperature. The higher the temperature, the faster the molecules are moving. You may remember that temperature is just a speedometer for molecules.


Sensing Temperature Overview: Have you ever wondered how an ice-cold glass of water gets water drops on the outside of the cup? It’s all about temperature change! You will see how a temperature difference can fool your fingers in today’s

hot and cold experiment.

What to Learn: You will understand why condensation occurs and feel how skin can detect a temperature difference, but not an exact temperature.

Materials

cup of hot water cup of cold water cup of room-temperature water

Experiment

1. Place one finger from one hand in the hot (not scalding) water. Place a finger from your other hand in the ice-cold water. Leave them there for a moment.

2. At the same time, take both fingers and place them in the room-temperature water. What do you feel?

3. Complete the data table.

Sensing Temperature Data Table

What do your fingers feel? Write your observations here!

Right Hand Finger Left Hand Finger Observations

Reading

Have you ever wondered how an ice-cold glass of water gets water drops on the outside of the cup? Where does that water come from? Does it ease its way through the glass? Did someone come by and squirt the glass with water? No, of course not. Some of the gaseous water molecules in the air came close enough to the cold glass to lose some molecular


speed. Since they lost speed, they formed bonds between each other and liquefied. They condensed on the cold surface of the glass.

Imagine, though, if you will, that you live several hundred years ago and the process of condensation wasn’t

understood. You happen to be an inquisitive, highly perceptive, person (which of course you are) and you notice

this film of water showing up on cold things. Water appearing out of apparently nowhere! You’d be pretty

amazed, wouldn’t you?!?

Isn’t it amazing that every time you pick up a cold can of soda there are molecular interactions happening right in

front of your eyes! This is why science is so wonderful. It provides the skills to see these amazing things and the

skills to investigate and perhaps understand them.

The skin contains temperature sensors that work by detecting the direction heat flows in or out of the body, but

not temperature directly. These sensors change temperature depending on their surroundings. When one finger

is heated up then placed in water at room temperature, the heat flows out of the body. The brain gets a message

saying the finger is cooler. A finger placed in ice water followed by room temperature water tells the brain it was

detecting a heat flow into your body… and presto! You have one confused brain.

In order for heat to flow, there must be a temperature difference. But why then do the metal legs of a table feel

colder than the wood tabletop when both are at the same room temperature? The metal will feel colder

because heat flows away from your skin faster into the metal than the wood. We’ll talk about heat capacity in a

later experiment, but this is why scientists had to invent the thermometer: The human body isn’t designed to

detect temperature, only heat flow.

Exercises

1. How did the hot finger feel when it was placed into the room-temperature water?

2. How did the cold finger feel when it was placed into the room-temperature water?


3. Based on your observations, what can you infer about how a skin detects temperature?

4. After taking a hot shower, a student noticed something interesting. When she put on her glasses and went into the hallway, her glasses fogged up with tiny droplets of water. What was happening?


Answers to Exercises

1. How did the hot finger feel when it was placed into the room‐temperature water? (cold)

2. How did the cold finger feel when it was placed into the room‐temperature water? (hot)

3. Based on your observations, what can you infer about how a skin detects temperature? (The skin detects temperature change but not the actual temperature.)

4. After taking a hot shower, a student noticed something interesting. When she put on her glasses and went

into the hallway, her glasses fogged up with tiny droplets of water. What was happening? (When she took her

warm glasses into the colder hallway, the air around her glasses cooled off, causing the air to change to drops of

liquid water.)


CHANGING MOLECULAR SPEEDS

You may have asked yourself the question, “So, if everything is made of molecules, and these molecules are often speeding up and slowing down… what happens to the stuff these molecules are made of if they change speed a lot? Will my kitchen table start vibrating across the room if the table somehow gets too hot?” No, it’s pretty unlikely that your table will begin jumping around the room, no matter how hot it gets. However, some interesting things do happen when molecules change speeds.


STATES OF MATTER

Matter has a tendency to hang out in fairly stable states under normal temperatures. There are three common states of matter; solid, liquid, and gas. How many states of matter do you see in this video with the balloon? If you want to do this experiment on the stove, heat a glass bottle in a saucepan (use about an inch of water in the pot and make sure there’s water both inside and outside the bottle). There is another state of matter called plasma but it is not common on Earth. Plasma is a highly energized gas. It is used in florescent lights. I’m going to assume you know a bit about solids, liquids and gasses so I won’t go into much detail about them here (see Unit 3 and Unit 8 for more information).


Balloon gymnastics

Overview: Heat causes all kinds of things to happen. We’ll zoom in on the micro scale of molecules as we explore in today’s lesson.

What to Learn: Heat energy influences all kinds of observable phenomena on our planet.

Materials

water

plastic bottle

balloon

stove top and saucepan or the setup in the video

Lab Time

1. Pour a couple of inches of water into an empty soda bottle and cap with a 7-9″ balloon. You can secure the balloon to the bottle mouth with a strip of tape if you want, but it usually seals tight with just the balloon itself.

2. Fill a saucepan with an inch or two of water, and add your bottle. Heat the saucepan over the stove with

adult help, keeping a close eye on it. Turn off the heat when your balloon starts to inflate. Since water has a

high heat capacity, the water will heat before the bottle melts. (Don’t believe me? Try the Fire-Water

Balloon Experiment first to see how water conducts heat away from the bottle!)

3. When you’re finished, stick the whole thing in the freezer for an hour. What happened to the balloon?

4. Record all observations in the worksheet

Balloon Gymnastics Observations

1. What happens to the balloon when the balloon is heated? What is happening to its air molecules?

2. What happens to the balloon when you put it in the freezer? What is happening with its molecules now?

http://www.sciencelearningspace.com/2010/09/fire-wate-balloon/




Reading

This material may be helpful to interpret today’s experiment:

Is it warmer upstairs or downstairs? The upstairs in a house is warmer because the pockets of warm air rise

because they are less dense than cool air. The more the molecules move around, the more room they need, and

the further they get spaced out. Think of a swimming pool and a piece of aluminum foil. If you place a sheet of foil

in the pool, it floats. If you take the foil and crumple it up, it sinks. The more compactly you squish the molecules

together, the denser it becomes.

As for why mountains and valleys are opposite, it has to do with the Earth being a big massive ball of warm rock

which heats up the lower atmosphere in addition to winds blowing on mountains and changes in pressure as you

gain altitude… in a nutshell, it’s complicated! What’s important to remember is that the Earth system is a lot bigger

than our bottle-saucepan experiment, and can’t be represented in this way.

Exercises Answer the questions below:

1. Draw a group of molecules at a very cold temperature in the space below. Use circles to represent each molecule.

2. True or False: A molecule that heats up will move faster.

a. True

b. False

3. True or False: A material will be less dense at lower temperatures.

a. True

b. False


Answers to Exercises: Balloon Gymnastics

1. Draw a group of molecules at a very cold temperature in the space below. Use circles to represent each molecule. (should be grouped very tightly)

2. True or False: A molecule that heats up will move faster (true)

3. True or False: A material will be less dense at lower temperatures (false)


MELTING AND EVAPORATION

What I do want to talk about is what happens as temperatures change in a substance. Let’s take one of the neatest substances on the Earth, water. Water is quite special since it can be in its solid, liquid and gas state at relatively “normal” temperatures. It’s quite special for a variety of other reasons too, but we’ll leave it at that for now. Pretend we have an ice cube on a frying pan (poor ice cube). Right now the water is in a solid state. It’s holding its shape. The molecules in the water are held together by strong, stiff bonds. These bonds hold the water molecules in a tight, very specific pattern called a matrix. This matrix holds the water molecules in a crystalline pattern and the solid water holds its shape. Now, let’s turn on the heat. The heat is transferred from the stove to the frying pan to the ice cube. (We’ll talk about heat transfer a bit later.) As the ice cube absorbs the heat the molecules begin to vibrate faster (the temperature is increasing). When the molecules vibrate at a certain speed (gain enough thermal energy) they stretch those strong, stiff bonds enough that the bonds become more like rubber bands or springs. When the bonds loosen up, the water loosens up and becomes liquid. There are still bonds between the molecules, but they are a bit loose, allowing the molecules to move and flow around each other. The act of changing from a solid to a liquid is called melting. The temperature at which a substance changes from a solid to a liquid is called its melting point. For water, that point is 32° F or 0° C. Now we will watch carefully as our ice cube continues to melt (little is more exciting than watching an ice cube melt – golf maybe). A bit after we see our ice cube go from solid to completely liquid, we notice bubbling. What’s going on now? If we were able to see the molecules of water at this point we’d be quite amazed at the fantastic scene before us. At 212° F or 100° C water goes from a liquid state to a gaseous state. This means that the loosey goosey bonds that connected the molecules before have been stretched as far as they go, can’t hold on any longer and “POW!” they snap. Those water molecules no longer have any bonds and are free to roam aimlessly around the room. Gas molecules move at very quick speeds as they bounce, jiggle, crash and zip around any container they are in. The act of changing from a liquid to a gas is called evaporation or boiling and the temperature at which a substance changes from a liquid to a gas is called its boiling point. This is a really cool experiment that shows you how to make clouds indoors (there’s a second experiment that uses a bike pump – watch that one also!):


Indoor Rain Clouds Overview: Today you get to vaporize liquid oceans of molecules and make it rain when the rising cloud decks hit the coldness of space. Sound like fun?

What to Learn: The movement of atmospheres on different planets is affected by the temperature of the planet and the molecules in the atmosphere.

Materials

Glass of ice water

Glass of hot water

Towel

Ruler

Experiment

1. Please be careful with this lab! The hot water can burn you!

2. Take two clear glasses that fit snugly together when stacked. (Cylindrical glasses with straight sides work well.)

3. Fill one glass half-full with ice water and the other half-full with very hot water (definitely an adult job –

and take care not to shatter the glass with the hot water!). Be sure to leave enough air space for the

clouds to form in the hot glass.

4. Place the cold glass directly on top of the hot glass and wait several minutes. If the seal holds between the

glasses, a rain cloud will form just below the bottom of the cold glass, and it actually rains inside the

glass! (You can use a damp towel around the rim to help make a better seal if needed.)

5. Complete the data table. Measure the water height carefully with your ruler. If you have 2” of water in the hot water glass, then write 2”. Please be careful when measuring hot water!


Indoor Rain Clouds Data Table

Hot Water Height Ice Water Height How well did it rain?

Reading

This experiment demonstrates state changes of matter. When hot vapor rises (like from the hot core of a gaseous

planet) and hits a cold front (like the coldness of outer space in the upper atmosphere), the vapor condenses into

liquid drops and rains, or can even freeze solid into ice chunks. Neptune and Uranus both have methane ice in their

upper atmospheres. Both Jupiter and Saturn have upper cloud decks of water vapor and clouds of ammonia. The

water vapor clouds are right at the freezing temperature of water.

Questions to Answer

1. Which combination made it rain the best? Why did this work?


2. Draw your experimental diagram, labeling the different components:

3. Add in labels for the different phases of matter. Can you identify all three states of matter in your experiment?


Answers to Exercises: Indoor Rain Clouds

1. Which combination made it rain the best? Why did this work? (The greater the temperature difference,

the better this experiment will work. The more water you have, the less the temperature will fluctuate for

each glass, thus making it able to rain for longer periods of time.)

2. Draw your experimental diagram here, labeling the different components:

3. Add in labels for the different phases of matter. Can you identify all three states of matter in your experiment? (Ice = solid; water = liquid, gas between two glasses is water vapor, nitrogen, and oxygen.)


CONDENSATION AND FREEZING

I don’t know about you, but I think it’s getting a bit hot in here. Let’s turn the heat down a bit and see what happens. If our gaseous water molecules get close to something cool, they will combine and turn from gaseous to liquid state. This is what happens to your bathroom mirror during a shower or bath. The gaseous water molecules that are having fun bouncing and jiggling around the bathroom get close to the mirror. The mirror is colder than the air. As the gas molecules get close they slow down due to loss of temperature. If they slow enough, they form loosey goosey bonds with other gas molecules and change from gas to liquid state. Here’s a cool trick magicians use when they open the freezer… The act of changing from gas to liquid is called condensation. The temperature at which molecules change from a gas to a liquid is called the condensation point.


Ghost coin

Overview: This spooky idea takes almost no time, requires a dime and a bottle, and has the potential for creating

quite a stir in your next magic show. The idea is basically this: when you place a coin on a bottle, it starts dancing

around. But there’s more to this trick than meets the scientist’s eye.

What to Learn: Heat energy is carried through different substances and affects the properties of different types of matter

Materials

Coin

Freezer

Plastic bottle (not glass)

Lab Time

1. Remove the cap of an empty plastic water or soda bottle and replace it with a dime.

2. Stick the whole thing upright in the freezer overnight. Make sure your group’s bottle is labeled! First thing in the morning, take it out and set it on the table. What happens?

3. Record all observations in the worksheet.

Ghost Coin Observations

Draw a picture of the water molecules inside of the water bottle when this experiment begins.


Now draw a picture of what they look like in the morning. What happened?


Reading

Matter has a tendency to hang out in fairly stable states under normal temperatures. There are three common

states of matter; solid, liquid, and gas. There is another state of matter called plasma, but it is not common on Earth.

Plasma is a highly energized gas. It is used in fluorescent lights. I’m going to assume you know a bit about solids,

liquids and gases so I won’t go into much detail about them here (see Unit 3 and 8 for more information).

What I do want to talk about is what happens as temperatures change in a substance. Let’s take one of the neatest

substances on the Earth, water. Water is quite special since it can be in its solid, liquid and gas state at relatively

“normal” temperatures. It’s quite special for a variety of other reasons, too, but we’ll leave it at that for now.

Pretend we have an ice cube on a frying pan (poor ice cube). Right now the water is in a solid state. It’s holding its

shape. The molecules in the water are held together by strong, stiff bonds. These bonds hold the water molecules

in a tight, very specific pattern called a matrix.

This matrix holds the water molecules in a crystalline pattern and the solid water holds its shape. Now, let’s turn

on the heat. The heat is transferred from the stove to the frying pan to the ice cube. (We’ll talk about heat transfer

a bit later.)

As the ice cube absorbs the heat, the molecules begin to vibrate faster (the temperature is increasing). When

the molecules vibrate at a certain speed (gain enough thermal energy) they stretch those strong, stiff bonds

enough that the bonds become more like rubber bands or springs. When the bonds loosen up, the water loosens

up and becomes liquid. There are still bonds between the molecules, but they are a bit loose, allowing the

molecules to move and flow around each other.

The act of changing from a solid to a liquid is called melting. The temperature at which a substance changes from a

solid to a liquid is called its melting point. For water, that point is 32° F or 0° C. Now we will watch carefully as our

ice cube continues to melt (little is more exciting than watching an ice cube melt – golf, maybe). A bit after we see

our ice cube go from solid to completely liquid, we notice bubbling. What’s going on now? If we were able to see

the molecules of water at this point we’d be quite amazed at the fantastic scene before us.

At 212° F or 100° C water goes from a liquid state to a gaseous state. This means that the loosey goosey bonds that

connected the molecules before have been stretched as far as they go, can’t hold on any longer and “POW!” they

snap. Those water molecules no longer have any bonds and are free to roam aimlessly around the room. Gas

molecules move at very quick speeds as they bounce, jiggle, crash and zip around any container they are in. The

act of changing from a liquid to a gas is called evaporation or boiling, and the temperature at which a substance

changes from a liquid to a gas is called its boiling point.

I don’t know about you, but I think it’s getting a bit hot in here. Let’s turn the heat down a bit and see what

happens. If our gaseous water molecules get close to something cool, they will combine and turn from gaseous to

liquid state. This is what happens to your bathroom mirror during a shower or bath. The gaseous water

molecules that are having fun bouncing and jiggling around the bathroom get close to the mirror. The mirror is

colder than the air. As the gas molecules get close, they slow down due to loss of temperature. If they slow

enough, they form loosey goosey bonds with other gas molecules and change from gas to liquid state.

The act of changing from gas to liquid is called condensation. The temperature at which molecules change from a gas to

a liquid is called the condensation point. Clouds are made of hundreds of billions of tiny little droplets of liquid water

that have condensed onto particles of some sort of dust. Now let’s turn the heat down a bit more and see what happens.

As the temperature drops and the molecules continue to slow, the bonds between the molecules can pull them together

tighter and tighter. Eventually the molecules will fall into a matrix, a pattern, and stick


together quite tightly. This would be the solid state. The act of changing from a liquid to a solid is called freezing, and the temperature at which it changes is called (say it with me now) freezing point.

Think about this for a second – is the freezing point and melting point of an object at the same temperature? Does

something go from solid to liquid or from liquid to solid at the same temperature? If you said yes, you’re right! The

freezing point of water and the melting point of water are both 32° F or 0° C. The temperature is the same. It just

depends on whether it is getting hotter or colder as to whether the water is freezing or melting. The boiling and

condensation point is also the same point. Now I’m going to mess things up a little bit. Substances can change

state at temperatures other than their different freezing or boiling points. Many liquids change from liquid to gas

and from gas to liquid relatively easily at room temperatures. And, believe it or not, solids can change to liquids

and even gases and vice versa at temperatures other than the usual melting, freezing, or boiling points. So what’s

the point of the points?

At a substance’s boiling, freezing, etc, points, all of the substance must change to the next state. The condition of

the bonds cannot remain the same at that temperature. For example, at 100° C water must change from a liquid to

a gas. That is the speed limit of liquid water molecules. At 100° C the liquid bonds can no longer hold on and all the

molecules convert to gas.


1. When a gas turns into a liquid, this is called:

a. Convection

b. Conduction

c. Absorption

d. Condensation

2. When water boils, what happens to the bonds between its molecules?


3. What is the best way to describe how the bonds between water molecules behave when in a liquid state?

a. Solid bridges

b. Rubber bands

c. No bonds

d. Brittle like chalk

4. The crystalline shape of a solid is referred to as:

a. a matrix

b. a vortex

c. a crystal

d. a cube


Answers to Exercises: Ghost Coin

1. When a gas turns into a liquid, this is called: (condensation)

2. When water boils, what happens to the bonds between its molecules? (They snap or break.)

3. What is the best way to describe how the bonds between water molecules behave when in a liquid state? (rubber bands or elastic)

4. The crystalline shape of a solid is referred to as: (a matrix)


WHAT ARE CLOUDS?

Clouds are made of hundreds of billions of tiny little droplets of liquid water that have condensed onto particles of some sort of dust. Now let’s turn the heat down a bit more and see what happens. As the temperature drops and the molecules continue to slow, the bonds between the molecules can pull them together tighter and tighter. Eventually the molecules will fall into a matrix, a pattern, and stick together quite tightly. This would be the solid state. The act of changing from a liquid to a solid is called freezing and the temperature at which it changes is called (say it with me now) freezing point. Think about this for a second – is the freezing point and melting point of an object at the same temperature? Does something go from solid to liquid or from liquid to solid at the same temperature? If you said yes, you’re right! The freezing point of water and the melting point of water are both 32° F or 0° C. The temperature is the same. It just depends on whether it is getting hotter or colder as to whether the water is freezing or melting. The boiling and condensation point is also the same point. Now I’m going to mess things up a little bit. Substances can change state at temperatures other than their different freezing or boiling points. Many liquids change from liquid to gas and from gas to liquid relatively easily at room temperatures. And, believe it or not, solids can change to liquids and even gases and vice versa at temperatures other than the usual melting, freezing, or boiling points. So what’s the point of the points?


CHANGING STATES AT UNUSUAL PLACES

At a substance’s boiling, freezing, etc, points, all of the substance must change to the next state. The condition of the bonds cannot remain the same at that temperature. For example, at 100° C water must change from a liquid to a gas. That is the speed limit of liquid water molecules. At 100° C the liquid bonds can no longer hold on and all the molecules convert to gas.


HEAT

Believe it or not, the concept of heat is really a bit tricky. What we call heat in common language, is really not what heat is as far as physics goes. Heat, in a way, doesn’t exist. Nothing has heat. Things can have a temperature. They can have a thermal energy but they can’t have heat. Heat is really the transfer of thermal energy. Or, in other words, the movement of thermal energy from one object to another. If you put an ice cube in a glass of lemonade, the ice cube melts. The thermal energy from your lemonade moves to the ice cube. Increasing the temperature of the ice cube and decreasing the temperature of your lemonade. The movement of thermal energy is called heat. The ice cube receives heat from your lemonade. Your lemonade gives heat to the ice cube. Heat can only move from an object of higher temperature to an object of lower temperature.


HEAT GOES FROM HOT TO COLD

Coffee cools down and ice water heats up. That’s one of the laws of thermodynamics. Do you remember what temperature is? Temperature measures how fast molecules are moving, right? Well, when heat transfers (moves) from one object to another, the movement of the molecules in the higher temperature object slow down and the movement of the molecules in the lower temperature object speed up. The liquid crystal sheet is temperature-sensitive. When the sheet received heat from the bulb, the temperature goes up and changes color. The plastic sheets remain black except for the temperature range in which they display a series of colors that reflect the actual temperature of the crystal. Here’s a neat experiment that uses this type of special thermal paper and a silver highlighter:


HEAT CAPACITY

Now let’s take explore how, even though heat can move from one object to another, it doesn’t necessarily mean that the temperature of the objects will change. You may ask, “What? Heat can move from one object to another without temperature changing one little bit?!?!” We’re going to take a look at one of the ways heat can move while the thermometer doesn’t. When things change phase (change from solid to liquid or liquid to gas or… well, you get the picture) the temperature of those objects don’t change. If you were able to take the temperature of water as it changed from a solid (ice) to a liquid you would notice that the temperature of that piece of ice will stay at about 32° F until that piece of ice was completely melted. The temperature would not increase at all. Even if that ice was in an oven, the temperature would stay the same. Once all the solid ice had disappeared, then you would see the temperature of the puddle of water increase. By the way, as the ice is melting, from where is heat being transferred? Heat is being transferred, by conduction, from the air. One key distinction is that objects don’t contain heat, but they contain energy. Heat is the transfer of energy from from one object to another, or from one system to another, like a hot cup of coffee to the cool ambient air. Heat can change the temperature of objects when it transfers the energy. In the example with the coffee cup, it lowered the temperature of the coffee. Imagine putting a sponge under a slowly running faucet. The sponge would continue to fill with water until it reached a certain point and then water started to drip from it. You could say that the sponge had a water capacity. It could hold so much water before it couldn’t hold any more and the water started dripping out. Heat capacity is how much heat an object can absorb before it increases in temperature. It’s often used interchangeably with “specific heat capacity”, but in reality it’s a little different.


SPECIFIC HEAT CAPACITY

Specific heat capacity is how much heat energy a mass of a material must absorb before it increases 1°C. It’s how much heat is needed to raise the temperature of 1 gram of the material. Heat Capacity is how much heat is required to raise the temperature. The units of heat capacity are J per Kelvin, whereas for specific heat capacity, the units are J per (gram-K). Each material has its own specific heat. The higher a material’s specific heat, the more heat it must absorb before it increases in temperature. Water is unique in that it has a very large specific heat. Liquid water’s specific heat is over 4 which is very high. In comparison, granite is 0.8, aluminum is 0.9, rubbing alcohol is 2.4 and gold is 0.1. To get the same amount of rubbing alcohol and liquid water to increase the same amount of temperature, you would need to pump about twice the amount of heat into the water. To get the same amount of gold and liquid water to increase the same amount of temperature, you would need to pump 40 times the amount of heat into the water!


FIRE WATER BALLOON

In other words, it takes more energy to heat water then it does to heat alcohol, gold, or for that matter most other things. Here’s a cool experiment you can do to really bring this idea alive that uses only water, a balloon, and a lit candle: Have you ever dipped a toe in the largest body of water on the planet… the Pacific Ocean? If you have, you know it’s colder than you’d expect, especially if it’s summer warm outside. It’s for two reasons, both of which are related to the heat energy equation:


Fire water balloon Overview: Heat energy can be observed in many ways. This simple experiment allows us to see how heat is transferred.

What to Learn: We’re exploring how heat energy can move between objects in a variety of ways.

Materials

Balloon

Water

Matches, candle, and adult help

Sink

Lab Time

1. Put the balloon under the faucet and fill the balloon with some water.

2. Now blow up the balloon and tie it, leaving the water in the balloon. You should have an inflated balloon with a tablespoon or two of water at the bottom of it.

3. Carefully light the match or candle and hold it under the part of the balloon where there is water.

4. Feel free to hold it there for a couple of seconds. You might want to do this over a sink or outside just in case!

5. Record observations in the worksheet below

Fire-Water Balloon Observations

1. What did the water do to the heat of the match?

2. Why didn’t the balloon pop? What does this tell you about heat energy in this system?


So why didn’t the balloon pop? The water absorbed the heat! The water actually absorbed the heat coming from

the match so that the rubber of the balloon couldn’t heat up enough to melt and pop the balloon. Water is very

good at absorbing heat without increasing in temperature, which is why it is used in car radiators and nuclear

power plants. Whenever someone wants to keep something from getting too hot, they will often use water to

absorb the heat.

Think of a dry sponge. Now imagine putting that sponge under a slowly running faucet. The sponge would continue

to fill with water until it reached a certain point and then water started to drip from it. You could say that the

sponge had a water capacity. It could only hold so much water before it couldn’t hold any more and the water

started dripping out. Heat capacity is similar. Heat capacity is how much heat an object can absorb before it

increases in temperature. This is also referred to as specific heat. Specific heat is how much heat energy a mass of

a material must absorb before it increases 1°C.

Reading

If you’ve ever had a shot, you know how cold your arm feels when the nurse swipes it with a pad of alcohol. What

happened there? Well, alcohol is a liquid with a fairly low boiling point. In other words, it goes from liquid to gas

at a fairly low temperature. The heat from your body is more than enough to make the alcohol evaporate.

As the alcohol went from liquid to gas, it sucked heat out of your body. For things to evaporate, they must suck in

heat from their surroundings to change state. As the alcohol evaporated, you felt cold where the alcohol was.

This is because the alcohol was sucking the heat energy out of that part of your body (heat was being transferred

by conduction) and causing that part of your body to decrease in temperature.

As things condense (go from gas to liquid state) the opposite happens. Things release heat as they change to a

liquid state. The water gas that condenses on your mirror actually increases the temperature of that mirror. This

is why steam can be quite dangerous. Not only is it hot to begin with, but if it condenses on your skin it releases

even more heat which can give you severe burns. Objects absorb heat when they melt and evaporate/boil. Objects

release heat when they freeze and condense.

Do you remember when I said that heat and temperature are two different things? Heat is energy – it is thermal

energy. It can be transferred from one object to another by conduction, convection, and radiation. We’re now

going to explore heat capacity and specific heat.

Water is very good at absorbing heat without increasing in temperature, which is why it is used in car radiators

and nuclear power plants. Whenever someone wants to keep something from getting too hot, they will often use water to absorb the heat.

Think of a dry sponge. Now imagine putting that sponge under a slowly running faucet. The sponge would continue

to fill with water until it reached a certain point and then water started to drip from it. You could say that the

sponge had a water capacity. It could only hold so much water before it couldn’t hold any more and the water

started dripping out. Heat capacity is similar. Heat capacity is how much heat an object can absorb before it

increases in temperature. This is also referred to as specific heat. Specific heat is how much heat energy a mass of a

material must absorb before it increases 1°C.



1. What is specific heat?

a. The specific amount of heat any object can hold

b. The amount of energy required to raise the temperature of an object by 1 degree Celsius.

c. The type of heat energy an object emits

d. The speed of a compound’s molecules at room temperature

2. Name two types of heat energy:

3. What type (or types) of heat energy is at work in today’s experiment?

4. True or False: Water is poor at absorbing heat energy.

a. True

b. False


Answers to Exercises: Fire Water Balloon

1. What is specific heat? (the amount of heat energy that material must absorb to increase in temperature 1 degree C)

2. Name two types of heat energy (conduction, convection, and radiation)

3. What type (or types) of heat energy is at work in today’s experiment? (radiation and convection)

4. True or False: Water is poor at absorbing heat energy. (false)


HOW MUCH ENERGY DOES A CANDY BAR HAVE?

How much energy does a candy bar have? How much energy does a candy bar have? If you flip it over and read the nutritional information on the back, you can figure it out with a little help from the video below:


HEAT FLOW

Let’s learn how to calculate the heat flow based solely on temperature readings from a thermometer (this is going to be important later in this lab):


HEAT AND STATES OF MATTER

Heat can also change the state of matter. When an ice cube melts into a liquid puddle, it remains at the same temperature until the phase change is complete, and only then does the temperature begin to rise, even though heat was added throughout the entire process. The thermometer reading will stay on the same temperature reading until the ice is completely melted.


SUBLIMATION

Carbon dioxide goes straight from a solid to a gas, which is called “sublimation”. It totally skips going through the liquid phase! How do you handle the transition from a solid block to a gas cloud? Here’s how: Did you know that eating a single peanut will power your brain for 30 minutes? The energy in a peanut also produces a large amount of energy when burned in a flame, which can be used to boil water and measure energy.


HEAT ENERGY OF A PEANUT

What makes up a peanut? Inside you’ll find a lot of fats (most of them unsaturated) and antioxidants (as much as found in berries). And more than half of all the peanuts Americans eat are produced in Alabama. We’re going to learn how to release the energy inside a peanut and how to measure it. Here’s what you do. If you don’t have the fancy equipment for the experiment, here’s a cheaper, easier way to do it using a candle and a paperclip…


Peanut Energy Overview: Put your safety goggles on for today’s lab –we’ll be looking at fire again. You’ll be measuring how much energy a peanut holds by setting it on fire and measuring an increase in water temperature.

What to Learn: All our energy needs on earth come from somewhere. We cannot make our own food, but

plants can. We are all connected to the plants and soils that they grow in because they provide our very basic needs, as well as some of our more modern needs.

Materials

Goggles 2 shelled peanuts Small pair of pliers Match or lighter Test tube in wire test tube holders (these look like pliers that are designed to hold a test tube) Scale Thermometer

Lab Time

1. Today we’re working with fire, so follow all special instructions provided about working with fire today.

2. Measure your test tube on the scale when it’s empty: _______________________ grams

3. Fill up your test tube with about 10 grams of water and weigh it again: _______________________ grams

4. Measure the initial temperature of the water: ___________________________ oC

5. Put on safety goggles.

6. Using a small pair of pliers, hold the peanut and ask an adult to light the peanut with the lighter until it catches fire.

7. Upon ignition (when the peanut is burning by itself and doesn’t need the lighter), hold the peanut under the water close to the bottom of the test tube until the peanut stops burning.

8. Quickly measure the final temperature of the water: ___________________________ oC

9. Record your results on the worksheet.

10. Allow the peanut to cool as you record your observations and complete the data tables.


Let's take an example measurement. Suppose you measured a temperature increase from 20 °C to 100 °C for 10

grams of water, and boiled off 2 grams. We need to break this problem down into two parts - the first part deals

with the temperature increase, and the second deals with the water escaping as vapor.

The first basic heat equation is this: Q = m c T

Q is the heat flow (in calories)

m is the mass of the water (in grams)

c is the specific heat of water (which is 1 degree per calorie per gram)

and T is the temperature change (in degrees)

So our equation becomes: Q = 10 * 1 * 80 = 800 calories.

If you measured that we boiled off 2 grams of water, your equation would look like this for heat energy: Q = L m

L is the latent heat of vaporization of water (L= 540 calories per gram)

m is the mass of the water (in grams)

So our equation becomes: Q = 540 * 2 = 1080 calories.

The total energy needed is the sum of these two:

Q = 800 calories + 1080 calories = 1880 calories.

Reading

Did you know that eating a single peanut will power your brain for 30 minutes? The energy in a peanut also produces

a large amount of energy when burned in a flame, which can be used to boil water and measure energy.

Peanuts are part of the bean family, and actually grow underground (not from trees like almonds or walnuts). In

addition to your lunchtime sandwich, peanuts are also used in woman's cosmetics, certain plastics, paint dyes,

and also when making nitroglycerin.

What makes up a peanut? Inside you'll find a lot of fats (most of them unsaturated) and antioxidants (as much as

found in berries). And more than half of all the peanuts Americans eat are produced in Alabama. We're going to

learn how to release the energy inside a peanut and how to measure it.

There's chemical energy stored inside a peanut, which gets transformed into heat energy when you ignite it. This

heat flows to raise the water temperature, which you can measure with a thermometer. You should find that your

peanut contains 1500-2100 calories of energy! Now don't panic - this isn't the same as the number of calories

you're allowed to eat in a day. The average person aims to eat around 2,000 Calories (with a capital "C"). 1 Calorie

= 1,000 calories. So each peanut contains 1.5-2.1 Calories of energy (the kind you eat in a day). Do you see the

difference?

So did all the energy from the peanut go straight to the water, or did it leak somewhere else, too? The heat actually

warmed up the nearby air, too, but we weren't able to measure that. If you were a food scientist, you'd use a nifty

little device known as a bomb calorimeter to measure calorie content. It's basically a well-insulated, well-sealed

device that catches nearly all the energy and flows it to the water, so you get a much more accurate temperature

reading. (Using a bomb calorimeter, you'd get 6.1-6.8 Calories of energy from one peanut!)


Peanut Energy Data and Observations

Trial # Mass of Water Temperature Increase Heat Energy 1 (calories)

(grams) (oC)

Sample 10 grams

80 oC

= (10 grams) x (1 degree per cal per gram) x 80 (oC)

= 800 calories

Trial # Mass of Water Boiled Off (grams) Heat Energy 2 (calories)

Sample

2 grams

=542calories per gram x 2 grams

= 1080 calories



Do Plants Store Energy?

Overview: Put your safety goggles on for today’s lab, because we’re working with fire! You’ll be measuring how much energy a peanut holds by setting it aflame.

What to Learn: All our energy needs on earth come from somewhere. We cannot make our own food, but plants can. We are all connected to the plants and soils that they grow in because they provide our very basic needs, as well as some of our more modern needs.

Materials

Goggles

2 shelled peanuts

Small pair of pliers

Match or lighter

Sink

Timer

Lab Time

1. Today we’re working with fire, so follow all special instructions about working with flames today.

2. bClose the drain with a sink stopper, and fill the sink with around an inch of water.

3. Put on safety goggles. Using a small pair of pliers, hold the peanut over the sink and ask your adult helper to light the peanut with the lighter until it catches fire. Have your data recorder ready with the timer.

4. Upon ignition (when the peanut is burning by itself and doesn’t need the lighter), start the timer and run it until the peanut stops burning. Record the time on the worksheet. The adult remains present for the entire

duration that the peanut is one fire.

5. Drop the peanut into the sink once finished to ensure all flames are out. Allow it to cool as you record additional observations in the worksheet and complete the exercises.


Do Plants Store Energy? Data and Observations

Observations:

Does the peanut burn with a clean flame or a sooty flame?

What color is the flame? What color does the peanut turn when it burns?

Did the size of the peanut change after it had burned for several minutes?

Reading

A peanut is not a nut, but actually a seed. In addition to containing protein, a peanut is rich in fats and carbohydrates. Fats and carbohydrates are the major sources of energy for plants and animals.

The energy contained in the peanut actually came from the sun. Green plants absorb solar energy and use it in photosynthesis. During photosynthesis, carbon dioxide and water are combined to make glucose. Glucose

is a simple sugar that is a type of carbohydrate. Oxygen gas is also made during photosynthesis.


The glucose made during photosynthesis is used by plants to make other important chemical substances needed for living and growing. Some of the chemical substances made from glucose include fats, carbohydrates

(such as various sugars, starch, and cellulose), and proteins.

Photosynthesis is the way in which green plants make their food, and ultimately all the food available on earth. All animals and non-green plants (such as fungi and bacteria) depend on the stored energy of green plants to live. Photosynthesis is the most important way animals obtain energy from the sun.

Oil squeezed from nuts and seeds is a potential source of fuel. In some parts of the world, oil squeezed from seeds-- particularly sunflower seeds--is burned as a motor fuel in some farm equipment. In the United States and elsewhere, some people have modified diesel cars and trucks to run on vegetable oils.

Fuels from vegetable oils are particularly attractive because, unlike fossil fuels, these fuels are renewable. They come from plants that can be grown in a reasonable amount of time. Fossil fuels are nonrenewable fuels

because they are formed over a long period of time.


1. What is the process called where plants get food from the sun?

a. Osteoporosis

b. Photosynthesis

c. Chlorophyll

d. Metamorphosis

2. Where does all life on the planet get its food?

3. List two ways that we could use the energy in a peanut:

a.

b.


Answers to Exercises: Do Plants Store Energy:

1. What is the process called in which plants get food from the sun? (photosynthesis)

2. Where does all life on the planet get its food? (plants, and the sun)

3. What can people use a peanut’s energy for? (fuel for cars, food)


THERMOSTAT

If you (or your parents) can remember thermostats before they became digital, then you may know about

bi-metallic strips, which is a piece of material made from of two strips of different metals which expand at

different rates as they are heated (usually steel and copper). The result is that the flat strip bends one way if

heated, and in the opposite direction if cooled. Normally, it takes serious skill and a red-hot torch to stick

two different metals together, but here’s a homemade version of this concept that your kids can make using

your freezer. The hardest part about this experiment is finding the right kind of bubble gum wrapper! Here

what you do:


TRIPLE POINT

The triple point is where a molecule can be in all three states of matter at the exact same time, all in equilibrium. Imagine having a glass of liquid water happily together with both ice cubes and steam bubbles inside, forever! The ice would never melt, the liquid water would remain the same temperature, and the steam would bubble up. In order to do this, you have to get the pressure and temperature just right, and it’s different for every molecule. The triple point of mercury happens at -38oF and 0.000000029 psi. For carbon dioxide, it’s 75psi and -70oF. So this isn’t something you can do with a modified bike pump and a refrigerator. However, the triple point of water is 32oF and 0.089psi. The only place we’ve found this happening naturally (without any lab equipment) is on the surface of Mars. Because of these numbers, we can get water to boil here on Earth while it stays at room temperature by changing the pressure using everyday materials. (If you have a vacuum pump, you can have the water boil at the freezing point of 32oF.) Here’s an experiment on how to boil room temperature water by changing the pressure:


CONDUCTION

In our example of the ice and the lemonade, it would work like this. The lemonade has a higher temperature than the ice. (The molecules are moving faster than the ice molecules.) The faster moving molecules of the lemonade would transfer heat to the ice causing the ice molecules to move faster (increase temperature) and eventually change from solid to liquid. In turn, since the faster moving molecules of the lemonade moves energy (transfers heat) to the ice, they slow down. This causes the temperature of your drink to decrease and that is what makes your lemonade nice and cold. Heat can be transferred in three different ways: conduction, convection and radiation. Let’s start with conduction. Heat is transferred through conduction the same way pool balls are scattered around a table in the opening break. On a pool table, one ball crashes into another ball which crashes into another ball speeding the balls up and moving them around the table. Heat transferred from one object to another through conduction does the same thing. The molecules near the heat source (candle, stove, etc.) begin moving faster (their temperature increases).


CONVECTION

As they move faster they crash into other molecules around them which cause them to move faster. As those molecules move faster they crash into more molecules…etc, etc. Thus the molecules in the object are all moving faster. Heat has been transferred by conduction and the temperature of the object is higher. Here’s a simple experiment using two water bottles and food coloring along with two different temperatures of water: Every time I’m served a hot bowl of soup or a cup of coffee with cream I love to sit and watch the convection currents. You may look a little silly staring at your soup but give it a try sometime!

Convection is a little more difficult to understand than conduction. Heat is transferred by convection by moving currents of a gas or a liquid. Hot air rises and cold air sinks. It turns out, that hot liquid rises and cold liquid sinks as well. Room heaters generally work by convection. The heater heats up the air next to it which makes the air rise. As the air rises it pulls more air in to take its place which then heats up that air and makes it rise as well. As the air get close to the ceiling it may cool. The cooler air sinks to the ground and gets pulled back near the heat source. There it heats up again and rises back up.


CONVECTION CURRENTS

This movement of heating and cooling air is convection and it can eventually heat an entire room or a pot of

soup. This next experiment should allow you to see convection currents – you can do this with a pot of

water on your stove if you don’t have access to the fancy chemistry equipment like I did in the video:


RADIATION

Heat is also transferred by radiation through electromagnetic waves. (We talked about waves and energy

in Unit 9.) Heat can be transferred by electromagnetic waves. Energy is vibrating particles that can move by

waves over distances right? Well, if those vibrating particles hit something and cause those particles to

vibrate (causing them to move faster/increasing their temperature) then heat is being transferred by

waves. The type of electromagnetic wave that transfer heat are infra-red (IR) waves. The Sun transfers heat

to the Earth through radiation. (There’s nothing between the Earth and the sun to conduct through or

convent with.)

Here’s a cool experiment that uses two different colors of paper and two ice cubes:


Soaking up Rays

Overview: It’s a blistering hot day and you want to wear something cool. Will you choose the dark- or light- colored outfit? Is there science involved in fashion? You bet!

What to Learn: You should discover that the sun transfers its heat in a process called radiation and that dark colors absorb the infrared radiation while light colors reflect it.

Materials

2 ice cubes, about the same size white piece of paper black piece of paper a sunny day

Experiment

1. Put the black paper and white paper on a sunny part of the sidewalk.

2. Put the ice cubes in the middle of the pieces of paper.

3. Wait. Record approximately how long it took for each ice cube to melt.

Soaking Up Rays Data Table

Color of Paper Size of Ice Cube Time to Melt

Reading


There are three ways to transfer heat: conduction, which means two objects touching; convection, where one of

the objects is a fluid like water or air; and radiation, which doesn’t need to be touching anything at all. Heat is

transferred by radiation through electromagnetic waves. Energy is vibrating particles that can move by waves over

a distance. If those vibrating particles hit something and cause those particles to vibrate, those particles begin to

move faster, causing a temperature increase. The types of electromagnetic waves that transfer heat are infra-red

waves.

If you hold your hand near an incandescent light bulb, you begin to feel heat on your hand. This is an example of heat traveling like a wave. This type of heat transfer is called radiation.

Now, don’t panic. This is not a bad kind of radiation like you get from X-rays. It’s infra-red radiation. Heat was

transferred from the light bulb to your hand. The energy from the light bulb caused the molecules in your hand to

resonate. Since the molecules in your hand are now moving faster, they have increased in temperature. Heat has

been transferred! In fact, an incandescent light bulb gives off more energy in heat than it does in light. They are not

very energy-efficient.

Now, if it’s a hot sunny day outside, are your students better off wearing a black or white shirt if they want to stay

cool? This experiment will help them figure it out. What they should eventually see is that the ice cube on the

black sheet of paper melts faster than the ice cube on the white sheet. Dark colors absorb more infra-red radiation

than light colors. Heat is transferred by radiation easier to something dark-colored than it is to something light-

colored and so the black paper increases in temperature more than the white paper.

So, to answer the shirt question, a white shirt reflects more infra-red radiation so it will stay cooler. White walls,

white cars, white seats, white shorts, white houses, etc. all act like mirrors for infra-red (IR) radiation. This is why

you can aim your TV remote at a white wall and still turn on the TV. Simply pretend the wall is a mirror (so you

can get the angle right), and bounce the beam off the wall before it gets to your TV. It looks like magic!

Exercises

1. How long did it take for the ice cube on black paper to melt? _____________________________

2. How long did it take for the ice cube on white paper to melt? _____________________________


3. What can you discover about light versus dark colors and the infra-red radiation of the sun based on this experiment?

4. What are three ways heat can be transferred?


Answers to Exercises

1. How long did it take for the ice cube on black paper to melt? (answers will vary)

2. How long did it take for the ice cube on white paper to melt? (answers will vary)

3. What can you discover about light verses dark colors and the infra‐red radiation of the sun based on this experiment? (Light colors reflect the infra‐red radiation of the sun, and dark colors absorb it.)


CALORIMETER

You can’t get through a science or engineering degree without having performed a calorimetry lab. A calorimetry experiment is made of of inexpensive equipment (it only uses a coffee cup and a thermometer) and the calculations needed to do the experiment are pretty easy, so you can already tell that teachers are going to like them. They are useful in figuring out the specific heat capacity and the heat of fucion or dissolution of an unknown substance (usually a lump of metal). Here’s how to make a coffee cup calorimeter and do the calculations: Chemists use a bomb calorimeter to measure the heat flow for reactions that involve gases (since the gases would escape out of the coffee cup) and reactions at high temperatures (which would melt the cup). It works the same way as the coffee cup version, only the reaction is sealed and placed in water, which is then placed in an insulated container. It’s a more elaborate setup as well as analysis because now you take into account the heat flow into the parts of the calorimeter. Heat also does work as it transfers energy.


HEAT ENGINES

Inventors have created many different types of heat engines that use heat transfer to do work, like spin a shaft. The engine in your car is an internal combustion engine. Geothermal devices, Stirling engines, thermionic devices, steam and hero engines are also devices that use heat transfer to do work. Before going over more detail about these, let’s take a break and build a few projects so you can see for yourself how useful heat is to do work!

The Drinking Bird is a classic science toy that dips its head up and down into a glass of water. It’s filled with a liquid called methylene chloride, and the head is covered with red felt that gets wet when it drinks. But how does it work? Is it perpetual motion? We’re going to modify one that will work on sunlight (or lamp light) instead of water:


Solar Drinking Bird Overview: The drinking bird is a classic science toy that dips its head up and down into a glass of water. It’s filled

with a liquid called methylene chloride, and the head is covered with red felt that gets wet when it drinks. But

how does it work? Is it perpetual motion? We’ll take a look at what’s going on with the bird, why it works, and

how we’re going to modify it so it can run on its own without using any water at all!

What to Learn: You’ll learn more about the sun than about the bird itself, and especially about the sun’s influence on the Earth, air, and water.

Materials

drinking bird

silver or white spray paint

black spray paint

razor

mug of hot water

sunlight or incandescent light

Lab Time

1. Take the bird out of its holder, and carefully remove the tail feather, hat, and felt section. Remove any glue

with a scraper or hot water, which will allow the glue to loosen and easily peel off. Be careful not to hold the bird by the head, because it is hollow and can break if you grip too tightly!

2. Paint the top (with the peak, from which the hat was removed) either white or silver. Paint the bottom black. Allow it to dry.

3. When the paint is dry, reattach the bird to its stand, and place it in the sun. Adjust the fastening band until the bird is secure, if needed.

4. Liquid is being heated now in the bird, so the bird will begin tipping as water begins moving from the

bottom to the top. The bottom of the bird is now black, and black absorbs more energy and heats up the

tail of the bird. Since the tail section is warmer, the pressure goes up and the liquid gets pushed up the

tube. By covering the head with white (or silver) paint, you are reflecting most of the energy so it remains

cool. Remember that white surfaces act like mirrors to IR light (which is what heat energy is).


Observations

1. What is happening to your drinking bird?

2. Does it work better with hot or cold water?

3. Does it work in an enclosed space, such as an inverted aquarium?

4. On a rainy day or dry?

5. In the fridge or on a heating pad?

Reading

The drinking bird in this experiment is an example of a heat engine. The liquid’s special properties allow the motion to continue, so long as there is some water provided to the system.

What’s so special about the liquid? Methylene chloride is made of carbon, hydrogen, and chlorine atoms. It’s barely

liquid at room temperature, having a boiling point of 103.5° F, so it evaporates quite easily. It does have a high

vapor pressure (6.7 psi), meaning that the molecules on the liquid surface leave (evaporate) and raise the

pressure until the amount of molecules evaporating is equal to the amount being shoved back in the liquid

(condensed) by its own pressure. (For comparison, the vapor pressure of water is only 0.4 psi.)

The bird needs a temperature difference between the head and tail. Since water needs heat in order to

evaporate, the head cools as the water evaporates. This temperature decrease lowers the pressure inside the

head, pushing liquid up the inner tube. With more liquid (weight in the head), the bird tips over. The bird wets

its own head to start this cycle again.

The trick to making this work is that when the bird is tipped over, the vapor from the bottom moves up the tube

to equalize the pressure in both sides, or he’d stay put with his head in the cup. Sadly, this isn’t perpetual motion

because as soon as you take away the water, the cycle stops. It also stops if you enclose the bird in a jar so water

can no longer evaporate after awhile. Do you think this bird can work in a rainstorm? In Antarctica?

Vapor pressure can also change with temperature changes. The vapor pressure goes up when the temperature

goes up. Since the wet head is cooler than the tail, the vapor pressure at the top is less than at the bottom, which

pushes the liquid up the tube. So it really does matter whether the bird is operating in Arizona or the Amazon. The

bird will dip more times per minute in a desert than a rain forest! This is because evaporation will work more

quickly in the desert.



1. Where does most of the energy on earth come from?

a. Underground

b. The sun

c. The oceans

2. What is one way that we use energy from the sun?

3. What is the process by which the liquid is being heated inside the bird?

a. Precipitation

b. Pressure

c. Evaporation

d. Transpiration


Answers to Exercises: Solar Drinking Bird

1. Where does most of the energy on earth come from? (the sun)

2. What is one way that we use energy from the sun? (plants, solar power)

3. What is the process by which the liquid is being heated inside the bird? (evaporation)


HERO ENGINE

There are lots of different kinds of heat engines, and they all use clever ways to convert a temperature difference into motion. Remember that the molecules in steam move around a lot faster than in an ice cube. So when we stick hot steam in a container, we can blow off the lid (used with pistons in a steam engine). or we can put a fan blade in hot steam, and since the molecules move around a lot, they start bouncing off the blade and cause it to rotate (as in a turbine). Or we can seal up hot steam in a container and punch a tiny hole out one end (to get a rocket). Here’s how to make a Hero Engine (the steam is enclosed in a vessel and allowed to jet out two (or more) pipes):


STIRLING ENGINE

Developed in 1810s, this engine was widely used because it was quiet and could use almost anything as a heat source. This kind of heat engine squishes and expands air to do mechanical work. There’s a heat source (the candle) that adds energy to your system, and the result is your shaft spins. This engine converts the expansion and compression of gases into something that moves (the piston) and rotates (the crankshaft). Your car engine uses internal combustion to generate the expansion and compression cycles, whereas this heat engine has an external heat source. This Stirling Engine project is a very advanced project that requires skill, patience, and troubleshooting persistence in order to work right. Find yourself a seasoned Do-It-Yourself type of adult (someone who loves to fix things or tinker in the garage) before you start working on this project, or you’ll go crazy with nit-picky things that will keep the engine from operating correctly. This makes an excellent project for a weekend.


Stirling Engine Overview: The Stirling heat engine is very different from the engine in your car. When Robert Stirling

invented the first Stirling engine in 1816, he thought it would be much more efficient than a gasoline or

diesel engine. However, these heat engines are used only where quiet engines are required, such as in

submarines or in generators for sailboats. You’re going to make one out of soda cans and old CDs.

What to Learn: A Stirling engine shows us how energy is converted and used to do work for us.

Materials

three soda cans pack of steel wool

old inner tube from a bike wheel drill with 1/16″ bit

super glue and instant dry pliers

electrical wire (3- conductor solid wire) scissors

3 old CDs razor

one balloon wire cutters

penny electrical tape

nylon bushing (from hardware store) push pin

small candle or alcohol burner permanent marker

fishing line (15lb. test or similar) Swiss army knife (with can opener option)

Lab Time

1. Open each soda can and empty the soda. Remove the top of one soda can with your can opener. This

work most easily by moving along the ridge on the can’s lid. Be careful not to cut yourself, so use adult

supervision.

2. Take the top off the second can in the same way, and then remove the bottom of the second can completely, about ¾ inch above the bottom. Use a sharp razor.

3. Cut the neck off a balloon to serve as the piston, and fit it over the lid of the can open at the top. Use a

rubber band to attach it at the top if needed. Now cut a square out of the inner tube that measures ¾

inch on each side. Glue the tube square on the center of the balloon and push down so it stays. To dry it

quickly, spray instant dry on it.

4. Take a pushpin and poke a hole in the center of the tube square. Set the can aside.

5. Take a water bottle cap and mark where we will drill holes. Mark one spot on the side of the cap

(about halfway up) and at an equal spot opposite. Also make a mark in the center of the cap. Drill the

holes with adult help, using pliers and a piece of wood to help make precise holes.


6. Attach the bottle cap to the opposite side of the diaphragm on the soda can (on the bottom), so take

the balloon off, and flip it upside down, stretching it over the lid again. The point of the pushpin

should point up, so thread it through the hole in the middle of the cap. Secure it with glue, and use

instant dry. Set this aside.

7. Grab the other can and prepare it for drilling. Make a mark about 1 inch down from the top of the can,

and make a similar mark on the exact opposite side of the can. Drill the holes, using a piece of wood to

help support the can if needed. Remember to use adult supervision!

8. Use the circular template and tape it in place to cut a viewing hole. You want the template secured so that it is not on the same side as the holes. Mark an outline where you will cut, and use a razor to cut it out.

9. Bend the wire in the shape of the crankshaft according to the template. Use pliers to help, cutting the

wire to about 8 inches to ensure a precise fit. Bend it with your fingers to match the template. Make

two marks according to the template and make marks on the wire. At this point, you will bend the

loop in the crankshaft 90 degrees, using two pairs of pliers this time. Make sure the ends of the

crankshaft are as flat and straight as possible. Orient and place the wire inside the can with the

viewing hole cut out. Check to make sure it can spin freely. Secure the ends with pieces of tape to stop

it from sliding out.

10. To make the displacer, take a 16-inch piece of copper wire, straightening it as much as possible. Use

pliers to create a small hook of about ½ inch. Use steel wool to roll the wire up. It should be the

diameter of the soda can once rolled up. Check that it fits into the bottom of the soda can with enough

clearance to fit in and out fairly easily. Use the pliers to work the copper wire to the height of the can.

11. Take your fishing line and cut off a few inches, tying it onto the loop of the wire in the displacer.

Secure it with superglue and instant dry if necessary. Thread the fishing line through the diaphragm.

Before you do this, take the diaphragm off and put it back on upside down, and pull the pushpin out,

threading the fishing line that the pushpin made. Place some oil around the wire so that it slides more

easily. Test it to see that there is no drag when you lift the whole displacer.

12. Nudge the displacer into the top of the soda can with the top cut off. Put the diaphragm over the top of

the can, making sure the bottle cap is centered. Test again to make sure the displacer falls freely. If it

doesn’t add more oil.

13. Take about 8 inches of copper wire and stick it through the holes in the sides of the bottle cap. Bend

each side of it with pliers. Make sure it can spin freely, so leave a gap on each side of the cap. Use

pliers again to bend the sides of the wires in towards the center of the cap, and then again so that it

can fit inside the other can. Both sides of the wire should touch the crankshaft in the can above.

14. Press the top can down around the bottom can gently. Don’t crush the can; we only want to ease it

down a bit further so that it is secure.


15. Secure the crank to the pushrods by orienting the long part towards the bottom of the can. Make a

mark about ½ inch higher than the spot where it rests on the crank. Trim the rods at these marks

with wire cutters. Allow the connecting rods to stick out the front, mark them about ¼ inch from the

end, and make hooks at these spots. Bend the hooks with pliers so that they stay on the crank. Loop

the hooks around the crank so that when spun, the push rods allow the displacer to move up and

down. Make sure the crank turns freely. If your balloon wants to push the rods up into the crank too

far, simply bend the corners in the push rods more sharply to shorten the rods. Be careful that the

fishing line doesn’t get caught.

16. Tie the fishing line to the middle of the big loop on the crank. Make sure the knot isn’t so tight that it

restricts the free movement of the crank as it turns. Tape the two strands of fishing line together, and

trim the loose ends of the line with scissors.

17. To make the flywheel, grab 3 old CDs or DVDs (anything by Michael Bay will work). Take your piece of

nylon bushing, which should be about ½ in diameter and 1 inch long. It should fit through the center

of the CD. Attach the CDs to the bushing (make sure it fits nice and snug).

18. Sand the end of the crankshaft so that it glues more easily. Hot glue this side to the nylon bushing,

generously gluing through the center of the bushing. Check to see that the flywheel spinning will

crank the engine.

19. Position the crank so that the large crank is facing downward. Attach a penny to the top surface of the

CD to serve as a counterweight. This will allow the engine to run more smoothly.

20. To make the engine’s base, cut the top and bottom off a can as we did before. Place a burner on the

inside at the bottom, and then tape it to the can. Make a hole for air with the razor in the side of the

can at about the level of the flame. Cut a few more holes in the side. They should be big enough so that

you can light the burner.

21. Assemble the engine on top of the burner base. Now we’re ready to test this thing, so remember to

put on safety goggles! Use a lighter to light the burner, and keep a hand on the top of the can to keep it

steady. If you need to give your engine a jump start, spin the flywheel.

22. Record your observations on the worksheet.


Stirling Engine Observations

1. What happens when you start the engine? What is going on?

2. Grab a cold bottle of water and pour a small amount into the top of the bottle cap. What happens? Why does this happen?

This engine was developed because it was quiet and could use almost anything as a heat source. This kind of

heat engine squishes and expands air to do mechanical work. There’s a heat source (the candle) that adds

energy to your system, and the result is your shaft spins (CD).

This engine converts the expansion and compression of gases into something that moves (the piston) and

rotates (the crankshaft). Your car engine uses internal combustion to generate the expansion and

compression cycles, whereas this heat engine has an external heat source.

Reading

Here’s how a Stirling engine is different from the internal-combustion engine inside your car. For example,

the gases inside a Stirling engine never leave the engine because it’s an external combustion engine. This

heat engine does not have exhaust valves as there are no explosions taking place, which is why Stirling

engines are quieter. They use heat sources that are outside the engine, which opens up a wide range of

possibilities from candles to solar energy to gasoline to the heat from your hand.

There are lots of different styles of Stirling engines. In this project, we’ll learn about the Stirling cycle and see

how to build a simple heat engine out of soda cans. The main idea behind the Stirling engine is that a certain

volume of gas remains inside the engine and gets heated and cooled, causing the crankshaft to turn. The gases

never leave the container (remember – no exhaust valves!), so the gas is constantly changing temperature and

pressure to do useful work. When the pressure increases, the temperature also increases. And when the

temperature of the gases decreases, the pressure also goes down. (How pressure and temperature are linked

together is called the “Ideal Gas Law”.)


Some Stirling engines have two pistons where one is heated by an external heat source like a candle and the

other is cooled by external cooling like ice. Other displacer-type Stirling engines have one piston and a

displacer. The displacer controls when the gas is heated and cooled.

This Stirling engine uses the heat from a coffee cup and the cooling from the ambient air.

In order to work, the heat engine needs a temperature difference between the top and bottom of the cylinder.

Some Stirling engines are so sensitive that you can simply use the temperature difference between the air

around you and the heat from your hand. Our Stirling engine uses temperature difference between the heat

from a candle and ice water.

The balloon at the top of the soda can is actually the ”power piston” and is sealed to the can. It bulges up as the gas expands. The displacer is the steel wool in the engine which controls the temperature of the air and allows air to move between the heated and cooled sections of the engine.

When the displacer is near the top of the cylinder, most of the gas inside the engine is heated by the heat

source and gas expands (the pressure builds inside the engine, forcing the balloon piston up). When the

displacer is near the bottom of the cylinder, most of the gas inside the engine cools and contracts. (The

pressure decreases and the balloon piston is allowed to contract.)

Since the heat engine only makes power during the first part of the cycle, there’s only two ways to increase the

power output: You can either increase the temperature of the gas (by using a hotter heat source), or by cooling the gases further by removing more heat (using something colder than ice).

Since the heat source is outside the cylinder, there’s a delay for the engine to respond to an increase or

decrease in the heat or cooling source. If you use only water to cool your heat engine and suddenly pop an ice

cube in the water, you’ll notice that it takes five to fifteen seconds to increase speed. The reason is because it

takes time for the additional heat (or removal of heat by cooling) to make it through the cylinder walls and into

the gas inside the engine. So Stirling engines can’t change the power output quickly. This would be a problem

when getting on the freeway!

In recent years, scientists have looked to this engine again as a possibility, as gas and oil prices rise, and exhaust

and pollutants are a concern for the environment. Since you can use nearly any heat source, it’s easy to pick one

that has a low-fume output to power this engine. Scientists and engineers are working on a model that uses a

Stirling engine in conjunction with an internal-combustion engine in a hybrid vehicle… maybe we’ll see

these on the road someday!


1. What is the primary input of energy for the Stirling engine?


2. As Pressure increases in a gas, what happens to temperature?

a. It increases b. Nothing c. It decreases d. It increases, then decreases

3. What is the primary output of the Stirling engine?


Answers to Exercises: Stirling Engine

1. What is the primary input of energy for the Stirling engine? (the candle)

2. As Pressure increases in a gas, what happens to temperature? (It increases.)

3. What is the primary output of the Stirling engine? (the moving piston)


IDEAL GAS LAW

The ideal gas law is important because you can predict how most gases with behave with a simple equation. Here’s how to do it:


Scientific Concepts we covered:

The terms hot, cold, warm etc. describe what physicists call thermal energy. Thermal energy is how much the molecules are moving inside an object. The faster molecules move, the more thermal energy that object has. There are different scales for measuring temperature: Fahrenheit, Celsius, Rankine and

Kelvin. Temperature is basically a speedometer for molecules. The faster they are wiggling and

jiggling, the higher the temperature and the higher the thermal energy that object has. Solids have strong, stiff bonds between molecules that hold the molecules in place. Liquids

have loose, stringy bonds between molecules that hold molecules together but allow them some flexibility. Gasses have no bonds between the molecules. Plasma is similar to gas but the molecules are very highly energized. Materials change from one state to another depending on the temperature and these bonds.

Changing from a solid to a liquid is called melting. Changing from a liquid to a gas is called boiling, evaporating, or vaporizing. Changing from a gas to a liquid is called condensation. Changing from a liquid to a solid is called freezing.

All materials have given points at which they change from state to state. Melting point is the temperature at which a material changes from solid to liquid. Boiling

point is the temperature at which a material changes from liquid to gas. Condensation point is the temperature at which a material changes from gas to liquid. Freezing point is the temperature at which a material changes from liquid to gas.

Heat is the movement of thermal energy from one object to another. Heat can only flow from an object of a higher temperature to an object of a lower temperature.

Heat can be transferred from one object to another through conduction, convection and radiation.

Conduction is the wiggle and bump method of heat transfer. Faster moving molecules bump into slower moving molecules speeding them up. Those molecules then bump into other molecules speeding them up and so on increasing the temperature of the object.

Convection is heat being transferred by currents of moving gas or liquid caused by hot air/liquid rising and cold air/liquid falling.

Radiation is the transfer of heat by electromagnetic radiation, specifically infra-red radiation.

When an object absorbs heat it does not necessarily change temperature. As objects change state they do not change temperature. The heat that goes into something as it’s changing phases is used to change the “bonds” between molecules. Freezing points, melting points, boiling points and condensation points are the “speed limits” of the phases. Once the molecules reach that speed they must change state.

Objects release heat as they freeze and condense. Objects absorb heat as they evaporate and melt.

Heat capacity is how much heat an object can absorb before its temperature increases. Specific heat is how much heat energy a mass of a material must absorb before it increases

1°C. Each material has its own specific heat. The higher a material’s specific heat is, the more

heat it must absorb before its temperature increases. Water has a very high heat capacity.

Yay! You’ve completed the lessons in Thermodynamics! Now it’s time to try your own problem set.


HOMEWORK PROBLEMS WITH SOLUTIONS

On the following pages is the homework assignment for this unit. When you’ve completed all the videos

from this unit, turn to the next page for the homework assignment. Do your best to work through as

many problems as you can. When you finish, grade your own assignment so you can see how much

you’ve learned and feel confident and proud of your achievement!

If there are any holes in your understanding, go back and watch the videos again to make sure you’re

comfortable with the content before moving onto the next unit. Don’t worry too much about mistakes at

this point. Just work through the problems again and be totally amazed at how much you’re learning.

If you’re scoring or keeping a grade-type of record for homework assignments, here’s my personal

philosophy on using such a scoring mechanism for a course like this:

It’s more advantageous to assign a “pass” or “incomplete” score to yourself when scoring your

homework assignment instead of a grade or “percent correct” score (like a 85%, or B) simply because

students learn faster and more effectively when they build on their successes instead of focusing on their

failures.

While working through the course, ask a friend or parent to point to three questions you solved correctly

and ask you why or how you solved it.

Any problems you didn’t solve correctly simply mean that you’ll need to go back and work on them

until you feel confident you could handle them when they pop up again in the future.

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vf

l � f = frequency v = speed l = wavelength

GEOMETRY AND TRIGONOMETRY

Rectangle A bh�

Triangle 12

A bh�

Circle 2A p�

2C p�r

r

Rectangular solid V wh� �

Cylinder

V rp� �2

2 2S r rp p� �� 2

Sphere 3

3V rp� 4

24S rp�

A = area C = circumference V = volume S = surface area b = base h = height � = lengthw = width r = radius

Right triangle

2 2 2c a b� �

sin ac

q �

cos bc

q �

tan ab

q �

c a

b90�q

CONSTANTS AND CONVERSION FACTORS

Proton mass, 271.67 10 kgpm ��

Neutron mass, 271.67 10 kgnm ��

Electron mass, 319.11 10 kgem ��

Avogadro’s number, 23 -10 6.02 10 molN � �

Universal gas constant, 8.31 J (mol K)R � �

Boltzmann’s constant, 231.38 10 J KBk ��

Electron charge magnitude, 191.60 10 Ce ��

1 electron volt, 191 eV 1.60 10 J�� Speed of light, 83.00 10 m sc � �

Universal gravitational constant,

11 3 26.67 10 m kg sG ��

Acceleration due to gravityat Earth’s surface,

29.8 m sg �

1 unified atomic mass unit, 27 21 u 1.66 10 kg 931 MeV c�� Planck’s constant, 34 156.63 10 J s 4.14 10 eV sh ��

25 31.99 10 J m 1.24 10 eV nmhc ��

Vacuum permittivity, 12 2 20 8.85 10 C N me ��

Coulomb’s law constant, 9 201 4 9.0 10 N m Ck pe� � � �

AVacuum permeability, 70 4 10 (T m)m p ��

Magnetic constant, 70 4 1 10 (T m)k m p ��

5 1 atmosphere pressure, 5 21 atm 1.0 10 N m 1.0 10 Pa� � � �

UNIT SYMBOLS

meter, m kilogram, kgsecond, sampere, Akelvin, K

mole, mol hertz, Hz

newton, Npascal, Pajoule, J

watt, W coulomb, C

volt, Vohm,

henry, H

farad, F tesla, T

degree Celsius, C� W electron volt, eV

2

A

�

�

PREFIXES Factor Prefix Symbol

1012 tera T

109 giga G

106 mega M

103 kilo k

10�2 centi c

10�3 milli m

10�6 micro m

10�9 nano n

10�12 pico p

VALUES OF TRIGONOMETRIC FUNCTIONS FOR COMMON ANGLES

q �0

�30

�37 45� �

53 60� 90�

sinq 0 1 2 3 5 2 2 4 5 3 2 1

cosq 1 3 2 4 5 2 2 3 5 1 2 0

tanq 0 3 3 3 4 1 4 3 3 �

The following conventions are used in this exam. I. The frame of reference of any problem is assumed to be inertial unless

otherwise stated. II. In all situations, positive work is defined as work done on a system.

III. The direction of current is conventional current: the direction in whichpositive charge would drift.

IV. Assume all batteries and meters are ideal unless otherwise stated.V. Assume edge effects for the electric field of a parallel plate capacitor

unless otherwise stated.

VI. For any isolated electrically charged object, the electric potential isdefined as zero at infinite distance from the charged object.

MECHANICS ELECTRICITY AND MAGNETISM

0x x xa tÃ Ã� �

x x� � 20 0Ãx t � a t

21

x

�2 20 2x x xa x xÃ Ã� � � 0

netFFa

m m� ��

��

f nF Fm��

2

carÃ�

p mv��

p F tD D��

212

K mv�

cosE W F d Fd qD � � ��

EPt

DD

�

20 0

12

t tq q w a� � �

0 tw w a� �

� � cos cos 2x A t A fw� � tp

i icm

i

m xx

m�

net

I Itt

a � ��

sinr F rFt �� q

L Iw�

L ttD D�

212

K Iw�

sF k x� ��

a = acceleration A = amplitude d = distance E = energy F = force f = frequency I = rotational inertia K = kinetic energy k = spring constant L = angular momentum � = lengthm = mass P = power p = momentum r = radius or separation T = period t = time U = potential energy v = speed W = work done on a system x = position y = height a = angular acceleration m = coefficient of friction q = angle t = torque w = angular speed

212sU kx�

gU mg yD D�

2 1Tf

pw

� �

2smTk

p�

2pTg

p� �

1 22g

m mF G

r�

�

gFg

m��

�

1 2G

Gm mU

r� �

1 22

0

14E

q qF

rpe�

�

EFE

q�

� �

20

14

qE

rpe�

�

EU q VD D�

0

14

qV

rpe�

VEr

DD

��

QV

CD �

0ACd

ke�

0

QE

Ae�

� 21 12 2CU Q V CD� � VD

QI

tDD

�

RAr� �

P I VD�

VIRD�

si

R R� i

1 1

p iiR R

�

pi

C C� i

1

s iC

� 1

iC

0

2IBr

mp

�

A = area B = magnetic field C = capacitance d = distance E = electric field e = emfF = force I = current � = lengthP = power Q = charge q = point charge R = resistance r = separation t = time U = potential (stored)

energy V = electric potential v = speed k = dielectric constant r = resistivity

q = angle F = flux

MF qv B� ��

�

sinMF qv q��

B

MF I B� ��

�

sinMF I Bq��

�

B B AF � � ��

cosB B AqF ��

B

te DF

D� �

B ve � �

�

FLUID MECHANICS AND THERMAL PHYSICS

A = areaF = force h = depth k = thermal conductivity K = kinetic energy L = thickness m = mass n = number of moles N = number of molecules P = pressure Q = energy transferred to a

system by heating T = temperature t = time U = internal energy V = volume v = speed W = work done on a system y = height�r = density

mV

r �

FPA

�

0P P gr� � �h

bF Vgr�

1 1 2 2A v A v�

21 1

12

P gy vr� �

22 2

12

P gy vr r� � �

1r

2

kA TQt L

DD

�

BPV nRT Nk T� �

32 BK k� T

VW PD� �

U Q WD � �

MODERN PHYSICS

E = energy f = frequency K = kinetic energy � = mass p = momentum l = wavelength f = work function�

E hf�

maxK hf f� �

hp

l �

2E mc�

WAVES AND OPTICS

d = separation f = frequency or

focal lengthh = height L = distance M = magnification m = an integer n = index of

refraction s = distance � = speed l = wavelength q = angle�

vf

l �

cnÃ

�

1 1 2sin sinn nq � 2q

1 1

i os s f� � 1

i

o

hM

h� � i

o

ss

L mlD �sind mq l�

GEOMETRY AND TRIGONOMETRY

A = area C = circumference V = volume S = surface area b = base h = height � = length w = width r = radius

Rectangle A � bh

Triangle 12

A b� h

Circle 2A rp�

2C rp�

Rectangular solid V w� � h

r

Cylinder 2V rp� �

22S rp p� �� 2

Sphere 34

3V p� r

24S rp�

Right triangle 2 2c a� � b2

sin ac

q �

cos bc

q �

tan ab

q �

c a

b90�q

ADVANCED PHYSICS COURSE CHAPTER 7: THERMODYNAMICS€¦ · CHAPTER 7: THERMODYNAMICS FOR HIGH SCHOOL PHYSICS CURRICULUM AND ALSO THE PREPARATION OF ACT, DSST, AND AP EXAMS This is

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