Document 2339816

Ben-Gurion University of the Negev
Department of Physics
Thermodynamics & Statistical Mechanics 1
‫גוריון בנגב‬-‫אוניברסיטת בן‬
‫המחלקה לפיסיקה‬
1 ‫תרמודינמיקה ומכניקה סטטיסטית‬
Thermodynamics and Statistical Mechanics I – Home Exercise 11
1.
Heat pump
a. Show that for a reversible heat pump the energy required per unit of heat delivered
inside the building is given by the Carnot efficiency
 
W
 C  h l . What
Qh
h
happens if the heat pump is not reversible?
b. Assume that the electricity consumed by a reversible heat pump must itself be
generated by a Carnot engine operating between the temperatures  hh and  l .
What is the ratio Qhh/Qh, of the heat consumed at  hh , to the heat delivered at  h ?
Give numerical values for Thh = 600K; Th = 300K; Tl = 270K
c. Draw an energy-entropy flow diagram for the combination heat engine-heat pump,
similar to Figures 8.1, 8.2 and 8.4 in Kittel, but involving no external work at all, only
energy and entropy flows at three temperatures
2.
Thermal pollution
A river with water temperature Tl=20oC is to be used as a low temperature reservoir of a
large power plant, with a steam temperature of Th=500oC. If ecological considerations limit
the amount of heat that can be dumped into the river to 1500MW, what is the largest
electrical output that the plant can deliver? If improvements in hot-steam technology would
permit raising Th by 100oC, what effect would this have on the plant capacity?
3.
Light bulb in a refrigerator
A 100W light bulb is left burning inside a Carnot refrigerator that draws 100W. Can the
refrigerator cool below room temperature?
4.
The Sargent Cycle
The diagram above is an approximation to a Sargent cycle run on an ideal gas. A constant
pressure path and a constant volume path are connected by two adiabatic paths. Assume all
processes are quasi-static and that the heat capacities, CP and CV, are constant.
a. Which of the four states (1-4) has the highest temperature and which has the
lowest?
b. T2 could be either hotter or colder than T4 depending on the specific values of P and
V at the four corners of the cycle. Demonstrate graphically one version of the cycle
Ben-Gurion University of the Negev
Department of Physics
Thermodynamics & Statistical Mechanics 1
‫גוריון בנגב‬-‫אוניברסיטת בן‬
‫המחלקה לפיסיקה‬
1 ‫תרמודינמיקה ומכניקה סטטיסטית‬
where T4 is clearly less than T2. Demonstrate another extreme where T4 would
necessarily be greater than T2
c. Prove that the efficiency of this cycle running as an engine is-   1  
T4  T1
,
T3  T2
where   C p / CV
d. Find an expression for the total work done, W, in one cycle. Express your results in
terms of N, kB,  , and the T’s
e. Show that the first law, QH  QC  W ,applied to this cycle (together with the
assumption that the heat capacities are constants) leads to the requirement that
CP  CV  NkB