Aheat engine operates between two reservoirs at 300k. during each cycle, it absorbs 200 calories from the high temperature reservoir. calculate:
(a) the maximum efficiency of the system
(b) the maximum works the engine can perform in each cycle

(a) Zero

The maximum efficiency (Carnot efficiency) of a heat engine is given by

where

is the low-temperature reservoir

is the high-temperature reservoir

For the heat engine in the problem, we have:

Therefore, the maximum efficiency is

(b) Zero

The efficiency of a heat engine can also be rewritten as

where

W is the work performed by the engine

is the heat absorbed from the high-temperature reservoir

In this problem, we know

Therefore, since the term cannot be equal to infinity, the numerator of the fraction must be zero as well, which means

W = 0

So the engine cannot perform any work.

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