Announcements 9/17/12 Prayer SPS Opening Social: Thursday 5-7 pm 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? Calvin & Hobbes

From warmup Extra time on? a. a.molar specific heat (e.g. why different depending on what you hold constant) b. b.total differential c. c.The book says that "This expression predicts a value of C v =3/2R=12.5 for all Monatomic gases", but the actual experimental C v values are also listed on the opposing page. When working problems, should we use the predicted universal value or the experimental actual value for C v of a Monatomic gas? Other comments? a. a.Out of curiosity, how is our TA 's name spelled? Does it have an accent like “Clément”? Cause his name is actually kind-of cool.

Clicker 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”

From warmup For each process discuss whether Q, W on, and ΔE int are positive, negative, or zero. a. a.Process 1-volume constant – – W=0, Q=+, E=+ b. b.Process 2 – – W=-, Q=+, E=+

Clicker 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

Clicker question: 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 Q = n C V  T (const. volume) Q = n C P  T (const. pressure)

Clicker 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 temperature by 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?

From warmup Explain why some modes (vibrational or rotational) do not contribute to the specific heat except at higher temperatures. a. a.The vibrational and rotational degrees of freedom of a molecule are not initiated until the molecule is subjected to higher levels of temperature so it doesn 't effective the specific heat of a molecule until it has is at higher temperatures. b. b.Not quite: “vibrational and rotational kinetic energies can only contribute to the specific heat when there is a significant amount of energy stored in them.”

Isothermal vs Adiabatic Isothermal: Adiabatic: What does gamma equal?  steeper curves for adiabatic

Clicker 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 Demo: adiabatic cotton burner

From warmup What does it mean to “take the total differential”? a. a.You take the derivative of every single variable in an equation b. b.Mostly correct: You take the derivative of both sides, using the product rule on the first side.

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?

Clicker question (like exam): 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.