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q=cv⋅T The heat capacity at a constant pressure is defined by : cp=∂h[j/kg⋅K] ∂T p Since the pressure is constant, the first law of thermodynamics can be rewritten as : q=u−W=up⋅v=h => cp=∂h=∂q ∂Tp ∂Tp and q=h=∫cp dT In the case where c p is constant, the gas is a “perfect gas”, and the equation can be rewritten : q=cp⋅T The relation between cp and cv can be obtained very easily using the ideal gas law and writing : cp=h=up⋅v=ur⋅T=cvr T T T 4.1.2 Entropy : Consider two points 1 and 2. A reversible path between those two points can always be defined, with a reversible heat transfer, and a reversible work. For example, an irreversible, adiabatic expansion from point 1 to point 2 can be simulated by a reversible heating up, and by a reversible work production (lower than the one that would have been produced in the reversible expansion). The first law states that : U2 –U1=QrevWrev The infinitesimal path in this evolution corresponds to : du=Qrev−p⋅dV 2 Qrev Qrev And since S2 – S1=∫1 T => dS= T It follows that : dU=T⋅dS−p⋅dV What can be expressed in terms of enthalpy as : dH=T⋅dSV dp 7PDF Image | An introduction to thermodynamics applied to Organic Rankine Cycles
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