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Answer :
The required Carnot engine performs 1318.31 J of work per cycle.
What is the Carnot engine?
The Carnot engine is an idealized heat engine that operates between two thermal reservoirs and is the most efficient engine possible for a given set of thermal reservoirs. The efficiency of a Carnot engine is given by the formula:
[tex]Efficiency = 1 - (T_{low} / T_{high})[/tex]
In this problem, the high-temperature reservoir is at 435 K and the low-temperature reservoir is at 280 K. Therefore, the efficiency of the Carnot engine is:
Efficiency = 1 - (280/435) = 0.3563 or 35.63%
The Carnot engine absorbs 3700 J of heat each cycle. Therefore, the work performed per cycle by the engine is:
Work = Efficiency * Heat absorbed
= 0.3563 * 3700 J = 1318.31 J
Therefore, the Carnot engine performs 1318.31 J of work per cycle.
Learn more about the Carnot engine here:
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