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Answer :
Final answer:
To operate an air conditioner that removes 1 Kilojoule of heat from a space with a coefficient of performance of 3, a reciprocating heat engine with a thermal efficiency of 35% needs to spend 0.94 Kilojoules of heat by burning fuel.
Explanation:
The thermal efficiency (η) of an engine is the proportion of the heat energy input that is converted into work, while the coefficient of performance (COP) of an air conditioner is the ratio of the cooling effect to the power input. Given η = 35%, this means that the engine converts 35% of the heat energy into work. Since the work produced by the heat engine is used to run the air conditioner which has a COP of 3, we can conclude that every 1 Kilojoule of work produced by the heat engine removes 3 Kilojoules of heat from the cooled space. If the air conditioner is to remove 1 Kilojoule of heat, then the work that the heat engine needs to produce is 1 Kilojoule / 3 = 0.33 Kilojoules. Since this work is 35% of the heat that must be spent by burning the fuel in the heat engine, we can calculate this heat as 0.33 Kilojoules / 35% = 0.94 Kilojoules.
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