4.2 Carnot Engine

It is a heat engine operating in a completely reversible manner.

Carnot cycle consists of two reversible isotherms and two reversible adiabats. Heat absorption by the amount \(Q_H\) is taking place at \(T_H\), and heat rejection by the amount \(Q_C\) is taking place at \(T_C\). Work is done by the working fluid during reversible adiabatic expansion, and work is absorbed by the working fluid during isothermal compression, and a net work is done by the working fluid.

\[\eta = \frac{W_{\text{net}}}{|Q_H|} = \frac{|Q_H|-|Q_C|}{|Q_H|} = 1 - \frac{T_C}{T_H}\]

  • Carnot cycle analysis says that:

    • Any difference \((T_H-T_C)\ne0 \) can be exploited to generate mechanical energy.

    • The greater the \((T_H-T_C)\) difference, the more efficient is the engine.

    • Energy waste is inevitable.

  • Carnot’s Principles:

    1. The efficiency of an irreversible heat engine is always less than the efficiency of a reversible one operating between the same two reservoirs.

    2. The efficiencies of all reversible heat engines operating between the same two reservoirs are the same.

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