An inventor claims to have developed a power cycle having a thermal efficiency of 40%, while operating between hot and cold reservoirs at temperature th and tc 5 300 k, respectively, where th is (a) 900 k, (b) 500 k, (c) 375 k. evaluate the claim for each case

Question

Physics

Annika Compton

8 November, 10:14

An inventor claims to have developed a power cycle having a thermal efficiency of 40%, while operating between hot and cold reservoirs at temperature th and tc 5 300 k, respectively, where th is (a) 900 k, (b) 500 k, (c) 375 k. evaluate the claim for each case

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Abagail Moran · Answer 1

From Carnot's theorem, for any engine working between these two temperatures:

efficiency < = (1-tc/th) * 100

Given: tc = 300k (from question assuming it is not 5300 as it seems)

For a, th = 900k, efficiency = (1-300/900) = 70%

For b, th = 500k, efficiency = (1-300/500) = 40%

For c, th = 375k, efficiency = (1-300/375) = 20%

Hence in case of a and b, efficiency claimed is lesser than efficiency calculated, which is valid case and in case of c, however efficiency claimed is greater which is invalid.