A Carnot heat engine and an ordinary refrigerator with coefficient of performance operate between reservoirs at and . The work done by the Carnot heat engine drives the refrigerator. If the heat engine extracts of energy from the hot reservoir, how much energy does the refrigerator exhaust to the hot reservoir?
The refrigerator rejects thermal energy to the hot reservoir.
Temperatures of the hot and cold reservoirs between which Carnot heat engine operates are: and respectively. The amount of heat extracted from the hot reservoir (source) is . Let the amount of heat rejected to the cold reservoir (sink) is and the amount of work done by the Carnot heat engine is . This heat engine drives a refrigerator whose coefficient of performance is . Let the amount of heat extracted from the cold reservoir (source) is , and the amount of heat rejected to the hot reservoir (sink) is .
Efficiency of a Carnot heat engine, ;Coefficient of performance of Carnot refrigerator,
Efficiency of the Carnot heat engine :
Thus, While amount of work input to the refrigerator Using this relation between and in coefficient of performance,
Conclusion: The refrigerator rejects 8.57J thermal energy to the hot reservoir.
A heat engine uses a diatomic gas that follows the cycle in FIGURE P.
a. Determine the pressure, volume, and temperature at point
b. Determine , and
for each of the three processes. Put your results in a FIGURE P table for easy reading.
c. How much work does this engine do per cycle and what is its thermal efficiency?
There has long been an interest in using the vast quantities of thermal energy in the oceans to run heat engines. A heat engine needs a temperature difference, a hot side and a cold side. Conveniently, the ocean surface waters are warmer than the deep ocean waters. Suppose you build a floating power plant in the tropics where the surface water temperature is . This would be the hot reservoir of the engine. For the cold reservoir, water would be pumped up from the ocean bottom where it is always . What is the maximum possible efficiency of such a power plant?
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