Announcements 9/13/10 5 students still haven’t registered their clickers. Be sure to

register them via the course website.a. Check your scores via the course website!

– Make sure you have scores listed under the “Clicker Quizzes” category.

Mathematica T-shirt today in honor of the first Mathematica problem due tonight. Mathematica is available in N212, N337, and possibly other computer labs.

a. To get into those two rooms, you need the combination from dept secretary Diann.

b. To use the computers in those rooms, you need a departmental computer account (form on dept website, under “computer support”).

I will hold my office hours in N337 today, and will go over the “Basic commands of Mathematica” handout from course website. Hopefully several computers will be available.

TA’s office hours still in underground lab.

Quick Writing

In light of what we discussed last lecture, how would you describe temperature on the microscopic level?

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”

How many molecules with speeds between 200 and 300 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

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. melty-freezy heatd. 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 -40 C, which part takes the most energy?

a. Raising the temperature b. Converting from solid to liquid

phasec. 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