Energy Part I: Introduction to Energy Chapter 7 Sec 1-3 of Jespersen 6 th ed)

Energy Part I:Introduction to Energy

Chapter 7 Sec 1-3of Jespersen 6th ed)

Dr. C. Yau

Spring 20131

Thermochemistry

Thermochemistry is a study of the heat flow in chemical reactions.

Kinetic versus Potential Energy

Kinetic Energy (KE) is the energy of motion.

KE = mv2 m=mass v=velocity

Potential Energy (PE) is "stored" energy

an object has that has the potential to be

changed to other forms of energy. 2

Forms of Energy

• kinetic energy

• potential energy

• heat (thermal E)

• light

• electrical

• nuclear

3

Chemical Energy

• Chemical Energy is a form of potential energy, due to the physical & chemical bonds within a substance

• A book has chemical energy. How can we get energy out of it?

4

Potential Energy

Potential energy depends on position:

e.g. Position of an object about to fall down, pulled by gravity.

e.g. Position of an object at a distance from an object to which it is attracted.

e.g. Position of a molecule/atom/ion/electron at a high energy level about to fall down to a lower energy level

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Potential Energy

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Consider a spring connecting two balls:

Natural position

It takes E to pull on the ball and stretch the spring out.From its extended position, the system has a higher potential energy.When the ball is released, the spring returns to its natural position, and the potential energy is released.What happens if you PUSH the balls together?

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Potential Energy

The potential energy of a spring depends on its length.Either stretching or squeezing the spring raises the P E. PE is at its lowest when the spring is at its natural length.

Factors Affecting Potential EnergyIncrease Potential Energy

• Pull apart objects that attract each other– Book/gravity

– N and S poles of magnets

– Positive and negative charges

• Push together objects that repel each other – Spring compressed

– N poles on two magnets

– 2 like charges8

Decrease Potential Energy

• Objects that attract each other come together– Book falls

– N and S poles of 2 magnets

– Positive and negative charges

• Objects that repel each other move apart– Spring released

– N poles on 2 magnets

– 2 like charges9

Factors Affecting Potential Energy

S N N S

S N N S

S N N S

Your Turn!Which of the following represents a decrease in the potential energy of the system?

A. A book is raised 6 feet above the floor.

B. A ball rolls downhill.

C. Two electrons come close together.

D. A spring is stretched completely.

E. Two atomic nuclei approach each other.

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1st Law of ThermodynamicsThe Conservation of Energy

Energy cannot be created nor destroyed.

It may be transformed into a different form of energy, but the total remains the same.

When you burn a book, what kind of transformations are there in terms of energy? How is energy conserved?

Etotal before reaction = E total after reaction

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Internal EnergyInternal energy (E) is the sum of energies for all of

the individual particles in a sample of matter.

It includes the "molecular kinetic energy": the kinetic energy of the particles in constant motion as they collide with each other and with the sides of the container.

ΔE is the change in internal energy during a process.

ΔE = Efinal – Einitial REMEMBER THIS!... Final minus Initial

In a reaction,

ΔE = Eproducts– Ereactants

We cannot measure E, but we can measure ΔE.12

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Temperature and Average Kinetic Energy

Large collection of molecules (gas) Wide distribution of kinetic energy (KE) Small number with KE = 0o Collisions momentarily stopped molecule’s

motion

Very small number with very high KEo Unbalanced collisions give high velocity

Most molecules intermediate KEs Result = distribution of energies

Kinetic EnergyAtoms and molecules are in constant random

motion.Within the sample each particle has different

kinetic energies, energies that are ever changing as they collide with each other and with the sides of the container.

HOWEVER, at a given temperature, the total energy & the AVERAGE KE of all the particles are constant.

The distribution of energy of the particles within the same follows the Boltzmann distribution.

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KE Distribution CurveThe KE distribution curve shows how the

fraction of particles with a given KE varies with KE.

The area under the curve corresponds to the sum of all the fractions = 1.

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The Bell Curve

If the KE were a Bell curve, the most probable KE would also be the average KE. However, the Boltzmann Distribution Curve is skewed.

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Boltzmann DistributionFig. 6.4 p.212

Any given sample would have a "most probable" KE. The AVERAGE KE is slightly to its right.

When temperature is increased, the graph flattens and shifts to the right.

At a higher temperature

Learn to draw this!

Most probable KEAverage KE

Most probable KE at the higher temperature

Average KE

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Boltzmann DistributionFig. 6.4 p.212

Of particular significance, the graph shows us that beyond the maxima, at the higher temperature, there are more molecules for a given KE.

At a higher temperature

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KE versus Temperature

The average KE is directly proportional to Temperature.

When T increases, heat is added to the sample and converted into the KE of the molecules.

The higher the T, the faster the gas particles are moving, proportionally.

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“State” of an Object• is a complete list of properties that specify

object’s current condition.

In Chemistry, “state” is defined by...

• Chemical composition (Number of moles of all substances present)

• Pressure

• Temperature

• Volume20

“State Function”"State function" is any property of a substance

that depends only on its current state and NOT on how it got there.

It is not dependent on the path taken to establish it.

For example, the mp of a substance is a state function.

The mp of ice is 0oC, regardless of how we get the ice, and what we did with the H2O before we changed it to ice.

Internal Energy is a "state function."

21Be sure you understand the meaning of “state function.”

State Function

• Location is a state function: both train and car travel to the same locations although their paths vary.

• The actual distance traveled does vary with path. Distance traveled is NOT a state function.

New York

Los Angeles

The time it took to get there...is that a state function? 22

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State Functions

• Some State functions in science:

Internal energy E = Ef – Ei

Pressure P = Pf – Pi

Temperature T = Tf – Ti

Volume V = Vf – Vi

Quick Review of ProportionalityMathematically, if we say x is proportional to

y, how do we express it in an equation?

Note: It is not accurate to say that if x increases and y increases, then x and y are directly proportional.

Why isn’t it? What is a better way to put it?

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Heat vs. TemperatureDo not confuse "heat" with "temperature."

It is easy to confuse the two because when we say it's "hot" we are actually referring to the temperature.

Heat is not temperature.

We can measure temperature (with a thermometer)

but we cannot measure heat directly.

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Heat• Pour hot coffee into cold cup

– Heat flows from hot coffee to cold cup

– Faster coffee molecules bump into wall of cup

– Transfer kinetic energy

– Eventually coffee & cup reach same temperature

Thermal Equilibrium• When both cup and coffee reach same

average Kinetic Energy and same temperature

– Energy transferred through heat comes from object’s internal energy

Heat versus T• Remember that we cannot determine E

(including thermal E, heat), but we can determine the CHANGE in E, ΔE.

ΔE for heat = q = amount of heat transferredIt is directly proportional to the change in T. q = CΔT

y = k xwhere C = heat capacityand ΔT = change in T

T final – T initial

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Heat Capacity vs. Specific Heat

Heat capacity = specific heat x mass

C = s x m

m = mass of the sample

s = specific heat,

a characteristic of the

sample.

Remember that q = C ΔTHere we have q = s m ΔT LEARN THIS!

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Specific Heat  Substance  

  Specific Heat,

J/ g °C (25 °C)  

  Carbon (graphite)     0.711  *

  Copper     0.387   *

  Ethyl alcohol  

  2.45  

  Gold     0.129   *

  Granite     0.803   *

  Iron     0.4498  *  

  Lead     0.128   *

  Olive oil     2.0  

  Silver     0.235   *

  Water (liquid)  

  4.18  

• It is the amt of heat needed to raise one gram of substance by one degree (either oC or K)

• Ones with * are all solids. What do their specific heats have in common?

• Substances with high specific heats resist temperature changes

• Note that water has a very high specific heat– (This is why coastal

temperatures are different from inland temperatures.) 29

Units of HeatThe SI unit of heat is the joule (J).It is equivalent to the amount of KE

possessed by 2 kg of object moving at a speed of 1 m/s:

KE = mv2

= (2 kg) (1 m/s)2

=1 kg m2 s-2

1 kJ = 1000 J1 cal = 4.184 J1kcal = 4.184 kJ1 kcal = 1 dietary Cal (called the Big Cal)

= 1 J (joule)

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Calculate the specific heat of a metal if it takes 235 J to raise the temperature of a 32.91 g sample by 2.53°C.

Cg

J82.2

C53.2g91.32

J235

t m

qs

t m sq

Note the units of specific heat:

J per gram per deg Celsius, or J g-1 oC-1.

It tells us how much heat is needed to raise 1 g of sample by 1 oC.

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Specific Heat of WaterThis is how the unit, calorie, was defined.

One calorie is the amount of heat needed to warm one gram (1 cc) of water by one degree (Celsius or K, kelvin)….

for example, to raise from 25oC to 26oC.

If we were to use K, it would be from 298 to 299K. Note that ΔT is the same regardless of whether it is in oC or K.

1 cal ≡ 4.184 J (We will stick to J and kJ.)32

The Sign of qq = amount of heat transferred

Heat can be either transferred INTO a system

or OUT OF a system.

q is positive if heat is going INTO a system.

q is negative if heat is going OUT OF a system.

Consider a hot cup of coffee. As it sits in the room, heat is going OUT OF the cup and INTO the surroundings.

qcup is negative and qsurr is positive

The value of q must be the same (amount of heat that goes into the surrounding must equal to the amount of heat that left the cup), but must have opposite signs. qsurr = - qcup 33

The Sign of q qsurr = - qcup

Note that the negative sign does NOT mean that qsurr

or qcup is negative.

It only means qsurr has an opposite sign to qcup.

e.g. If the cup loses 4 J as it cools down, the surroundings have gained 4 J.

qcup = – 4 J (Cup lost 4 J)

qsurr = + 4 J (same quantity but – (– 4J)

(same amt of heat, but sign is changed)34

The Sign of qNow, let’s consider a can of cold soda warming

up to room temperature, absorbing 5 J.This equation still holds true… qsurr = – qcan

qcan = + 5 J

(The can gained 5 J)qsurr = – (+5 J) (same amt of heat, but sign is

changed) (Surrounding is giving away 5 J.) 35