State Kelvin Planck and Clausius statement and establish the equivalence of both for second law of thermodynamics.

Mumbai university > Mechanical Engineering > Sem 3 > Thermodynamics

Marks: 8M

Year: Dec 2015

1 Answer

Kelvin-Planck statement:“It is impossible to construct an engine, which while operating in a cycle produces no other effect except to extract heat from a single reservoir and do equivalent amount of work”. Clausis Statement: “It is impossible for a self acting machine working in a cyclic process unaided by any external agency, to convey heat from a body at a lower temperature to a body at a higher temperature”. Although the Clausius and Kelvin-Planck statements appear to be different, they are reallyequivalent in the sense that a violation of either statement implies violation of other.

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Fig.1: Equivalence of Clausius statement to Kelvin-Planck statement.

Refer Fig.1. Consider a higher temperature reservoir T1 and low temperature reservoir

T2. Fig.1 shows a heat pump which requires no work and transfers an amount of Q2 from a low temperature to a higher temperature reservoir (in violation of the Clausius statement). Let an amount of heat Q1 (greater than Q2) be transferred from high temperature reservoir to heat engine which develops a net work, W = Q1 – Q2 and rejects Q2 to the low temperature reservoir. Since there is no heat interaction with the low temperature, it can be eliminated. The combined system of the heat engine and heat pump acts then like a heat engine exchanging heat with a single reservoir, which is the violation of the Kelvin-Planck statement.

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