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# Carnot Cycle Efficiency in an Idea Gas

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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.

© BrainMass Inc. brainmass.com October 4, 2022, 12:53 pm ad1c9bdddf
https://brainmass.com/physics/entropy/carnot-cycle-of-an-ideal-gas-and-it-s-efficiency-182953

## 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 = &#951; = 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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This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

© BrainMass Inc. brainmass.com October 4, 2022, 12:53 pm ad1c9bdddf>
https://brainmass.com/physics/entropy/carnot-cycle-of-an-ideal-gas-and-it-s-efficiency-182953