Physics H133: Problem Set #18

Here are some hints, suggestions, and comments on the problem set.

Two-Minute Problems

Remember to give a good explanation, no longer than two sentences.

1. T8T.7: Is helium gas monatomic or diatomic? Check equation (T8.8): Does U or N change during the compression?
2. T9T.1: Check whether energy is conserved or not (do you get as much back as you put in).

Chapter T Problems

• T8B.6: There is a termperature change, but is work done? How do we calculate entropy in this case?
• T8B.7: Does the temperature of the water change? Does equation (T8.21) apply?
• T8R.1: In T8.1, the energy En is proportional to n2. What is it for an Einstein solid? For the gas, we divided by N! because the atoms are not distinguishable. Is this true for an atom in a solid?
• T9B.3: An application of the basic efficiency formula based on a temperature difference.
• T9B.5: What happens to the waste heat?
• T9B.6: Think of the energy flow for an insulated room with a refrigerator inside (plugged into external electricity). A refrigerator works by taking heat out of a cold reservoir and putting it into a hot reservoir; what are these reservoirs in this case?
• T9S.14: (a) Step 1 is isothermal, so what does that say about heat in versus work out? Can you calculate the work? (b) Isothermal again, but what signs are the work and heat? (c) Just apply it the equation. (d) How can you eliminate TH and TC from the (T9.18) equations? (e) Put it all together in e = (|QH|-|QC|)/|QH|.
• T8A.1: (a) What is the volume, energy, and number of molecules of each gas before removing the barrier? What are the numbers after? Calculate the change in entropy without the N! term. (b) Plug the same quantities into the Sackur-Tetrode equation to find the entropy change. (c) If molecules are indistinguishable, what is the difference at the macroscopic level between two gases with N molecules each in volume V and one gas with 2N molecules in volume 2V? Note that we want to identify distinguishable microstates.