A heat engine extracts of heat from the hot reservoir each cycle and exhausts of heat. What are (a) the thermal efficiency and (b) the work done per cycle?
(a) The thermal efficiency is 27 %
(b) The work done per cycle is .
(a) The ratio of work done per cycle to amount of heat retrieved from the warm reservoir is the efficiency of the engine. The difference between the extracted heat and the work done per cycle equals the work done per cycle. and exhausted heat so we have
work done W per cycle is the difference of heat extracted and heat dumped into cold reservoir .
Substitute 15 kJ for W and 55 kJ for in the equation of efficiency above.
(b) The work done per cycle, as explained is difference of heat extracted and heat dumped into cold reservoir.
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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