Announcements 1/19/11 Prayer Regarding the TA’s comments about ( ) vs [ ] vs { } — Those were specifically about how to get Mathematica to work properly.

Announcements 1/19/11 Prayer Regarding the TA’s comments about ( ) vs [

] vs { } — Those were specifically about how to get Mathematica to work properly. You don’t have to use those symbols that way in the handwritten homework that you turn in. (At least one student asked Chris about that.)

One HW paper with no CID… anyone claim? One lab with incorrect CID… wrote down

617… anyone claim? Today’s newspaper article

Characterizing velocities Recall bouncing balls in jar. Focus on one

type of molecule. Lots of questions, such as :

a. What’s the average velocity? b. What’s the most popular velocity?c. What’s the velocity that corresponds to

the average kinetic energy?d. How many molecules have velocities

within a given range?How to answer: use statistical distributions, aka histograms

Height Histogram (made up data): Total students = 49 Round heights to closest

integer, plot histogram What is the combined area

of all bars? If I pick a student at random,

what are chances he/she will be 68 inches tall?

What is the area of the bar at 68 inches divided by the total area?

How many students will be exactly 68.000000 inches tall?

If I pick a student at random, what are chances he/she will be 61.5-64.5 inches tall?

What is average height of all students? (At least, how would you figure that out?)

“Normalized” Histogram: Total students = 49 Y-axis now divided by

total # of students. What is combined

area of all bars? If I pick a student at

random, what are chances he/she will be 61.5-64.5 inches tall? (At least, how would you figure that out?)

How many students have heights between 61.5 and 64.5 inches?

What is average height of all students?

Probability Distribution Function

Imagine total # =10 billion. Tiny “bins”. Connect peaks of curve with line… becomes a function

What is combined area of all bars? If I pick a person at random, what are chances he/she will

be 63.6-67.2 inches tall? How many people have heights between 63.6 and 67.2

inches? What is average height of all people? (If a non-symmetric

curve, this is not just the peak of the curve.)

Velocity Distribution: “Maxwell-Boltzmann”

At 600K, how many molecules with speeds between 400 and 600 m/s?

What is “vmost probable”? What is “vaverage”? What is “vrms”? How many molecules

are at exactly the “most probable” velocity?

2122( ) Bmv k Tf v v e

with some constantsout in front tonormalize itWhere does this eqn come from? Wait a few weeks.

Calvin and Hobbes, Bill Watterson

Calvin and Hobbes, Bill Watterson

Calvin and Hobbes, Bill Watterson

An ideal gas has a mixture of heavy and light monatomic molecules at the same temperature. Which molecules will have the most kinetic energy (on average)?

a. heavyb. lightc. same

Thought question

Heat = not a fluid!

Sir Benjamin Thompson, Count Rumford, 1753-1814

a. Boiling water with a cannon

Image credit: Wikipedia

James Joule, 1818-1889

Image credit: Wikipedia

Demo/Video

Demo: Boiling water with a vacuum

Video: Boiling water in a paper cup

Reading Quiz What name do we give to the heat

capacity per unit mass? a. entropy b. internal energyc. mass-pacityd. normalized heat capacitye. specific heat

Specific Heat

Q=mcT

Thought Question If you add 500 J of

heat to a mass of water, and 500 J of heat to the same mass of copper, which one increases the most in temperature?

a. Waterb. Copperc. Same

Reading Quiz

Thermal energy that is used to melt or freeze something is called:

a. latent heatb. mass heatc. mass-pacityd. molar heate. specific heat

Phase Changes

T

Heat energy added (Q)

100o C Water boils

0o C Ice melts

Ice warming

Ice melting

Water warming

Water boiling

Steam warming

Latent Heats

Thought Question If you want to melt a cube of ice

that’s initially at -40C, you must first raise its temperature to 0C, and then you must melt it. Which part takes the most energy?

a. Raising the temperature b. Meltingc. Same

Calorimetry

Worked problem (class designed):____ grams of hot iron at _____ C is added to ____ g of water at _____ C in a styrofoam insulated container. What is the final temperature of the mixture? (Neglect the container.)

ciron = 448 J/kgC cwater = 4186 J/kgC Lwater-steam = 2.26 106 J/kg