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# Thermodynamics: Efficiency of a Carnot cycle

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I need a calculation of the 'Carnot cycle' and a proof of the 'efficiency expression.

Efficiency expression: e = benefit / cost = W / Q Q = heat absorbed

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The solution gives detailed calculations to prove the expression for efficiency of a Carnot cycle.

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Thermal physics(schroeder) : carnot cycle
I need a calculation of the 'Carnot cycle' and a proof of the 'efficiency expression;. DETAILED please

Efficiency expression: e = benefit / cost = W / Q Q = heat absorbed

As we know the Carnot cycle is the combination of four processes
i) Isothermal expansion (A to B)
ii) Adiabatic expansion (B to C)
iii) Isothermal compression (C to D) and
iv) Adiabatic compression (D to A)
The thermodynamic states of the n moles of ideal gas taken as working substance are given as the coordinates.
i) Isothermal expansion (A to B)
The thermodynamic state changes from (P1V1T1) to (P2V2T1) i.e. the pressure and the volume changes while the temperature remains same T1 as that of the source.
The work done in isothermal change at temperature T1, as the volume changes from V1 to V2 is given by
W1 = n R T1 ln (V2/V1) -------------------------- (1)
As there is no change in the temperature of the gas, there will be no change in its internal energy and hence the work done by the gas is equal to the energy absorbed by the gas ...

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