SI Problem SessionsT 3-4W 12-2Th 5-6:30Regener 111

Correction to SISchedule:

Why are you cold getting out of a swimming pool when there is a light breeze?

a) Moisture on your skin has good thermal conductivityb) Water has a high heat capacityc) This is a purely psychological effect from sensing

wetness and airflowd) The water on your skin is colder than the surrounding

aire) It takes 540 calories to evaporate a gram of water; this

heat comes from your body

The way to determine pressure using the kinetic-molecular model of a gas is:

a) Calculate the kinetic energy and then use the principle of virtual work

b) Recognize that there is no heat flow in an isolated system

c) Determine the acceleration of each molecule and use F=ma

d) Determine how many molecules strike the wall per second, and use the change in momentum of each, with F = dP/dt

e) Recognize that if the gas causes the wall to move a distance dx, the work is F dx and this is equal to the loss in kinetic energy of the gas molecules

For a monatomic ideal gas, we can show that

the product pV

= 2/3 of the translational kinetic energy of the molecules, Ktr!

So nRT = (2/3)Ktr

Temperature is proportional to the kinetic energy per molecule.

20 liters of Argon are in thermal equilibrium with 20 liters of Helium. (These are monatomic gases, Mar=40, Mhe=4.)

Which molecules have more kinetic energy, on average?

A] Argon

B] Helium

C] Both have the same

Which molecules are moving faster, on average?

Late Homework: Lose 1/3 per day. BUT… never worth less than 1/3.

Do the homework ON TIME,but if you forget or absolutely can’t,DO IT ANYWAY.

The kinetic energy of n moles of gas depends ONLY on temperature.

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K tr =32 nRT

Heat = energy.If we add heat to an ideal gas (held at constant V), it gets warmer.The energy we add goes into increased kinetic energy of the molecules.

What is the “heat capacity” (specific heat, but per mole) for a monatomic ideal gas?

Also, Q = nCvT

So the “molar heat capacity at constant volume” is€

K = 32 nRΔT =Q

€

Cv =32 R

Equipartition of EnergyThe kinetic energy associated with x motion of the gas molecules is

or per molecule

The kinetic energy associated with y motion is

The kinetic energy associated with z motion is

The kinetic energy associated with spring stretching (in a diatomic) is

The kinetic energy associated with relative motion along the bond direction (in a diatomic) is

€

12 nRT

€

12 kBT

€

12 kBT

€

12 kBT

€

12 kBT

€

12 kBT

The effects of quantum mechanics: some motions require a “minimum energy”.

Memorize: translation (in a gas) is free, rotation is cheaper than vibration

Quantum effect

Which has more internal energy: A mole of N2 at 100°C or a mole of He at 100°C?

A] NitrogenB] Both have the same energy since T is sameC] Helium

Which has more internal energy, 1 liter of N2 at 1 atm

Or 1/2 liter of N2 at 2 atm? (each with 1 mole of gas)

A] 1 liter at 1 atmB] both have the same internal energyC] 1/2 liter at 2 atm

W= Work Done BY a Gas =

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pdVV1

V2

∫Memorize!

When gas does work, it loses internal energy

(unless energy is added, via heat.)

When it does negative work, it gains internal energy

A gas in a piston is taken from state 1 to state 2. The outside pressure is higher than the pressure in the cylinder.

For which path does the gas do the largest positive work?

For which path does the gas do the most negative work?(I.e. for which path is the most work done ON the gas)

Or chooseE] no path does work of this sign

In the isobaric process shown, W is:

A] +

B] -

C] 0

D] cannot determine

In the isobaric process shown, U is:

In the isobaric process shown, Q is:

In the isochoric process shown, W is:

A] +

B] -

C] 0

D] cannot determine

In the isochoric process shown, U is:

In the isochoric process shown, Q is:

In the isothermal process shown, W is:

A] +

B] -

C] 0

D] cannot determine

In the isothermal process shown, U is:

In the isothermal process shown, Q is:

Let’s do this quantitatively.