# 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.

- T8T.7: Is helium gas monatomic or diatomic?
Check equation (T8.8): Does U or N change during the compression?
- 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 E
_{n} is proportional to n^{2}.
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 T
_{H}
and T_{C} from the (T9.18) equations? (e) Put it all together
in e = (|Q_{H}|-|Q_{C}|)/|Q_{H}|.
- 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.

Your comments and
suggestions are appreciated.

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**Physics H133: Hints for Problem Set 18.**

Last modified: 05:05 pm, May 05, 2012.

furnstahl.1@osu.edu