# Carnot Cycle Efficiency in an Idea Gas

Please see the attached problem on how to show the efficiency of a Carnot cycle of an ideal gas using its entropy-temperature diagram. Maximum efficiency must then be estimated.

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

Let S1 and S2 be the two entropy values on the diagram.

The total amount of thermal energy transferred between the hot reservoir and the system =

= Qh = T2 * (S2 - S1)

and the total amount of thermal energy transferred between the system and the cold reservoir=

= Qc = T1 * (S2-S1)

The amount of energy transferred as work = W = Qh - Qc = (T2 - T1) * (S2 - S1)

The efficiency = η = W/Qh = (T2 - T1)/T2 = 1 - (T1/T2)

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Here, T2 = 800 K,

T1 = Boiling point of water = 100 deg. C = 272+100 = 372 K

Henve, efficiency = 1 - 372/800 = 53.5%

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