Announcements 9/19/11 Prayer HW: Your responsibility is NOT just to get the right answer, it’s to persuade Chris you know what you’re doing Answer this question 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 even possible? How can you compress a gas without its temperature increasing? Frank & Ernest

Thought Questions A gas has its pressure reduced while its volume is kept constant. What does this look like on a PV diagram? a. a.a horizontal line going to the right b. b.a horizontal line going to the left c. c.a vertical line going up d. d.a vertical line going down Same situation. How did the temperature of the gas change during that process? a. a.the temperature increased b. b.the temperature decreased c. c.the temperature stayed the same d. d.the temperature change cannot be determined from the information given

Demo Constant volume change, aka “alcohol rocket”

Thought question How will the temperature of the gas change during this process from A to B? a. a.Increase b. b.Decrease c. c.First increase, then decrease d. d.First decrease, then increase e. e.Stay the same

Worked Problem (by class) A diatomic ideal gas undergoes the change from A to B. How much heat was added to or taken away from the gas? (First: was heat added or taken away?) Answer: J

Reading quiz What is “C V ”? a. a.heat capacity b. b.molar heat capacity c. c.molar heat capacity, but only for constant volume changes d. d.specific heat e. e.your “curriculum vitae”, a detailed resumé Q = n C V  T (const. volume) Q = n C P  T (const. pressure)

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--does it take more heat to increase 1  C if volume is constant or if pressure is constant?) a. a.constant volume b. b.constant pressure c. c.they are the same

C V and C P Constant volume change (monatomic): W = 0  E int = Q added (3/2)nR  T = Q added Compare to definition of C: Q added = nC V  T C V = (3/2)R (monatomic) Constant pressure change a. a.What’s different? b. b.result: C P = (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: a. a.C P + C V b. b.C P - C V c. c.C V - C P d. d.C V / C P e. e.C P / C V

Isothermal vs Adiabatic Isothermal: Adiabatic:  steeper curves for adiabatic

Thought question How much would the temperature of the air in this room would change if I compressed it adiabatically by a factor of 2? (V 2 = 1/2 V 1 ) a. a.less than 0.2 degree C b. b.about 0.2 degrees C c. c.about 2 degree C d. d.about 20 degrees C e. e.more than 20 degrees C

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

Derivation of PV  (for Monatomic)  E int = Q added + W on (3/2) nR  T = -  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 V 5/3 = 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? a. a. b. b. c. c. d. d. e. e.