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# Homework A by pgh12747

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```									                                       Homework A
PHY4523                                                             Due: January 29, 2010

Each problem 10 pts.

1. (11.3)

2. An explosive liquid at temperature 300 K contains a spherical bubble of radius 5 mm,
full of its vapor. When a mechanical shock to the liquid causes adiabatic compression of
the bubble, what radius of the bubble is required for combustion of the vapor, given that
the vapor ignites spontaneously at 1100°C? The ratio CV/nR is 3.0 for the vapor.

3. (12.5) Work with one mole of an ideal gas. Assume the initial temperature is Ti and
express the final temperature Tf in terms of Ti. The part (b) could be little bit tricky. The
initial state is gas on the left chamber at Ti, V, and P. Now you do work on the gas
pushing it through the valve the other chamber at constant pressure P. Since work is
done on the gas and dQ = 0 in this process, the temperature of the gas in the right
chamber should rise and reach your final state when the left chamber volume is reduced
to v. Equate the work done on the system in this process to ∆TCp(1-v/V). Think about the
meaning this expression.

4. (13.4)

5. (13.8) In a steady state, the heat loss per unit time should be balanced by the heat
input by the heat pump.

6. (14.4) (a) and (b) only.

7. (14.7) Do not work on the part (b) for the van der Waals gas.

8. Derive all four Maxwell’s relations for a soap film whose differential internal energy
is written as
dU = Tds + γ dA
where γ is the surface tension and A is the surface area of the film.

9. You want to boil a pot of water at 20°C heating to
100°C. There are two ways of doing this: (1)
irreversibly by simply putting the pot in contact with                             T = 373 K
100°C heat reservoir (2) heating the pot of water in a
reversible manner. The 2nd law of thermodynamics                         dQ1
dictates that the total entropy of the system (pot of
water + the heat reservoir) would increase in method
(1). I suggest a way of heating the pot in a reversible                C                  dW
manner: simply inserting a Carnot engine between the
reservoir and the pot (see the figure).

Water
dQ2
at T
The Carnot engine operates between two temperatures, absorbing heat dQ1 from the
100°C reservoir and rejecting dQ2 to the water at temperature T (heat capacity Cp). At
the same time, work dW has to be generated in this process. Starting from 20°C water
temperature, delivering heat in this manner reversibly, the pot of water reached at 100°C.
(a) Show that the total entropy of the whole system (reservoir + water) remains the same
in this process. Ignore the heat capacity of the pot and the temperature dependence of the
water heat capacity.
(b) How much work is produced in this process?

10. (3.4)

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