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Announcements 1/26/11

- Prayer
- Please do this “Quick Writing” assignment while you’re waiting for class to start:
Ralph is confused because he knows that when you compress gases, they tend to heat up (think of a bicycle pump nozzle getting hotter as you force the gas from the pump to the tire). So, how are “isothermal” processes possible? How can you compress a gas without its temperature increasing?

Demo

- Constant volume change, aka “alcohol rocket”

Thought question

- How will the temperature of the gas change during this process from A to B?
- Increase
- Decrease
- First increase, then decrease
- First decrease, then increase
- Stay the same

Reading quiz

- What is “CV”?
- heat capacity
- mass-pacity
- molar heat capacity
- molar heat capacity, but only for constant volume changes
- your “curriculum vitae”, a detailed resumé

Thought question

- Which will be larger, the molar heat capacity for constant volume changes or the molar heat capacity for constant pressure changes? (Hint: Think of the First Law.)
- constant volume
- constant pressure
- they are the same
- it depends on the temperature

CV and CP

- Constant volume change (monatomic):
W = 0

Eint = Qadded

(3/2)nRT = Qadded

Compare to definition of C: Qadded = nCVDT

CV = (3/2)R (monatomic)

- Constant pressure change
- What’s different?
- result: CP = (5/2)R (monatomic)

- What would be different for gases with more degrees of freedom?

Reading quiz (graded)

- What does gamma equal in the equation for an adiabatic process:
- CP + CV
- CP - CV
- CV - CP
- CV / CP
- CP / CV

Isothermal vs Adiabatic

- Isothermal:
- Adiabatic:
steeper curves for adiabatic

Thought question

- How much do you think the temperature of the air in this room would change by if I compressed it adiabatically by a factor of 10? (Vf = V0/10)
- less than 0.1 degree C
- about 0.1 degrees C
- about 1 degree C
- about 10 degrees C
- more than 10 degrees C

Demo/Video

- Demo: freeze spray
- Video: adiabatic expansion
- Demo: adiabatic cotton burner

Derivation of PVg (for Monatomic)

Eint = Qadded + Won

(3/2) nRT = - PdV

(3/2) nRdT = -PdV

(3/2) nR d(PV/nR) = -PdV

(3/2) (PdV + VdP) = -PdV

(3/2) VdP = -(5/2) PdV

dP/P = -(5/3) dV/V

lnP = (-5/3)lnV + constant

lnP = ln(V-5/3) + constant

P = constant V-5/3 (it’s a different constant)

P V5/3 = constant

What’s different

if diatomic?

Thought question

- Which of the curves on the PV diagram below is most likely to represent an isothermal compression, followed by an adiabatic expansion back to the initial volume?

Thought questions

- What would be the molar specific heat for an adiabatic process? (Hint: think of Q = nCDT.)
- CV
- CV + R
- CV + 2R
- CV - R
- none of the above

- What would be the molar specific heat for an isothermal process? (Same hint.)
- CV
- CV + R
- CV + 2R
- CV - R
- none of the above

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