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Chapter 4: 4.10 (page 129)
Suppose that heat leaks into your kitchen refrigerator at an average rate of 300 watts. Assuming ideal operation, how much power must it draw from the wall?
The power drawn from wall is 57.69 W.
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Prove that if you had a heat engine whose efficiency was better than the ideal value (4.5), you could hook it up to an ordinary Carnot refrigerator to make a refrigerator that requires no work input.
Consider an ideal Hampson-Linde cycle in which no heat is lost to the environment.
(a) Argue that the combination of the throttling valve and the heat exchanger is a constant-enthalpy device, so that the total enthalpy of the fluid coming out of this combination is the same as the enthalpy of the fluid going in.
(b) Let be the fraction of the fluid that liquefies on each pass through the cycle. Show that
where is the enthalpy of each mole of compressed gas that goes into the heat exchanger, is the enthalpy of each mole of low-pressure gas that comes out of the heat exchanger, and is the enthalpy of each mole of liquid produced.
(c) Use the data in Table to calculate the fraction of nitrogen liquefied on each pass through a Hampson-Linde cycle operating between 1 bar and 100 bars, with an input temperature of . Assume that the heat exchanger works perfectly, so the temperature of the low-pressure gas coming out of it is the same as the temperature of the high-pressure gas going in. Repeat the calculation for an input temperature of .
A small scale steam engine might operate between the temperatures and , with a maximum steam pressure of bars. Calculate the efficiency of a Rankine cycle with these parameters.
A power plant producesof electricity, at an efficiency of (typical of today's coal-fired plants).
(a) At what rate does this plant expel waste heat into its environment?
(b) Assume first that the cold reservoir for this plant is a river whose flow rate is .By how much will the temperature of the river increase?
(c) To avoid this "thermal pollution" of the river, the plant could instead be cooled by evaporation of river water. (This is more expensive, but in some areas it is environmentally preferable.) At what rate must the water evaporate? What fraction of the river must be evaporated?
A heat pump is an electrical device that heats a building by pumping heat in from the cold outside. In other words, it's the same as a refrigerator, but its purpose is to warm the hot reservoir rather than to cool the cold reservoir (even though it does both). Let us define the following standard symbols, all taken to be positive by convention:
(a) Explain why the "coefficient of performance" (COP) for a heat pump should be defined as Qh / W.
(b) What relation among Qh , Qc, and W is implied by energy conservation alone? Will energy conservation permit the COP to be greater than 1 ?
(c) Use the second law of thermodynamics to derive an upper limit on the COP, in terms of the temperatures Th and Tc alone.
(d) Explain why a heat pump is better than an electric furnace, which simply converts electrical work directly into heat. (Include some numerical estimates.)
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