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carnot=1 – tc th The Clausius theorem can be rewritten for the specific case of the Carnot engine, using the thermodynamic temperature scale : ∫Qrev=qh −qc =0 T Th Tc Which demonstrates the Clausius relation in the particular case of the Carnot cycle 3.2 Non reversible engines In the case of a non reversible engine, irreversibilities lower the work output and thus increase the heat rejected at the heat sink : wwrev qcqc ,rev => eta=1 – qh etacarnot=1 – qc qh qc ,rev and ∫Q=qh−qc∫Qrev TThTc T Which leads to the Clausius inequality : ∫Q ≤0 T The relation accounts for any fluid evolution in an isolated system. It is useful to define a state variable accounting for that relation. The entropy is therefore defined by : 2 Qrev S=∫1 T =S2−S1 3.3 The increase of entropy principle In a nonreversible process going from points 1 to 2, the Clausius inequality can be written for the cycle 1 – 2 1: Q2Q1Q 2Q ∫ =∫ ∫ rev=∫ S1−S2≤0 cycle T 1 T 2 T 1 T 5PDF Image | An introduction to thermodynamics applied to Organic Rankine Cycles
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