Question

briefly describe a carnt cycle and derive an expression for the efficiency of carnot cycle

Answer 1

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Answer 2

The Carnot cycle consists of the following four processes:

A reversible isothermal gas expansion process. In this process, the ideal gas in the system absorbs qin amount heat from a heat source at a high temperature Th, expands and does work on surroundings.
A reversible adiabatic gas expansion process. In this process, the system is thermally insulated. The gas continues to expand and do work on surroundings, which causes the system to cool to a lower temperature, Tl.
A reversible isothermal gas compression process. In this process, surroundings do work to the gas at Tl, and causes a loss of heat, qout.
A reversible adiabatic gas compression process. In this process, the system is thermally insulated. Surroundings continue to do work to the gas, which causes the temperature to rise back to Th.
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Efficiency

The Carnot cycle is the most efficient engine possible based on the assumption of the absence of incidental wasteful processes such as friction, and the assumption of no conduction of heat between different parts of the engine at different temperatures. The efficiency of the carnot engine is defined as the ratio of the energy output to the energy input.


efficiency=net work done by heat engineheat absorbed by heat engine=−wsysqh(1.1)

=nRThln(V2V1)+nRTlln(V4V3)nRThln(V2V1)(1.2)

Since processes II (2-3) and IV (4-1) are adiabatic,

(T2T3)CV/R=V3V2(1.3)

and

(T1T4)CV/R=V4V1(1.4)

And since T1 = T2 and T3 = T4,

V3V4=V2V1(1.5)

Therefore,

efficiency=nRThln(V2V1)−nRTlln(V2V1)nRThln(V2V1)(1.6)

efficiency=Th−TlTh(1.7)