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Derivation of Efficiency of Carnot Cycle with Arbitrary Gas Equation of State

Hui Yi

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Abstract

In most textbooks of thermodynamics,the Carnot efficiency is derived with the ideal gas as its working substance,which is done by calculating the heats involved in two isothermal processes and using the associated adiabatic relation for the ideal gas.In this paper,with the same procedure,the Carnot efficiency is calculated regardless of the functional form of the gas equation of state.It can be used as a supplementary teaching material for undergraduate students.

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What this paper is about

In most textbooks of thermodynamics,the Carnot efficiency is derived with the ideal gas as its working substance,which is done by calculating the heats involved in two isothermal processes and using the associated adiabatic relation for the ideal gas.In this paper,with the same procedure,the Carnot efficiency is calculated regardless of the functional form of the gas equation of state.It can be used as a supplementary teaching material for undergraduate students.

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Available abstract

In most textbooks of thermodynamics,the Carnot efficiency is derived with the ideal gas as its working substance,which is done by calculating the heats involved in two isothermal processes and using the associated adiabatic relation for the ideal gas.In this paper,with the same procedure,the Carnot efficiency is calculated regardless of the functional form of the gas equation of state.It can be used as a supplementary teaching material for undergraduate students.

Key concepts: Carnot cycle, Adiabatic process, Ideal gas, Thermodynamics, Isothermal process, Ideal (ethics), Equation of state, Mathematics

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