Thermodynamics and Statistical Mechanics I - Home Exercise 11

Thermodynamics and Statistical Mechanics I - Home Exercise 11
1. Absorption refrigerator
In absorption refrigerators the energy driving the process is supplied not as work, bus as
heat from a gas flame at a temperature τhh > τh . Mobile home and cabin refrigerators
may be of this type, with propane fuel.
(a) Give an energy-entropy flow diagram similar to Figures 8.2 and 8.4 in Kittel for
such a refrigerator, involving no work at all, but with energy and entropy flows at
the three temperatures τhh > τh > τI .
(b) Calculate the ratio
Qhh/Q
h
for the heat extracted at τ = τI , where Qhh is the heat
input at τ = τhh . Assume reversible operation.
2. Photon Carnot engine
Consider a Carnot engine that uses as a working substance a photon gas.
(a) Given τh and τI as well as V1 and V2 , determine V3 and V4 .
(b) What is the heat Qh taken up and the work done by the gas during the first
isothermal expansion? Are they equal to each other, as for the ideal gas?
(c) Do the two isentropic stages cancel each other, as for the ideal gas?
(d) Calculate the total work done by the gas during one cycle. Compare it with the
heat taken up at τh and show that the energy conversion efficiency is the Carnot
efficiency.
3. Room air conditioner
A room air conditioner operates as a Carnot heat pump. Outside temperature is Th
and the room temperature is Tl . The room is not thermally isolated and heat leaks in
at a rate of A(Th − TI ). This is removed from the room by the air conditioner, which
runs at a power P .
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(a) Show that in steady state, the room temperature is given by the following relation-
TI =
P
Th +
2A
"
−
P
Th +
2A
#1/2
2
−
Th2
(b) For outside temperature of 37◦ C, room temperature of 17◦ C, air conditioner
power of P = 2 kW, find the heat-loss coefficient A of the room in W K −1 .
(c) We now turn off the air conditioner. How long will it take for the room temperature
to be 36◦ C (number of air molecules in the room is ≈ 5 × 1026 )?
4. Light bulb in a refrigerator
A 100 W light bulb is left burning inside a Carnot refrigerator that draws 100 W. Can
the refrigerator cool below room temperature?
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