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2 Q ∫1 T≤S The additional increase of entropy is due to an internal irreversible heat generation during the process (for example : friction losses in a turbine, pressure drops, etc.) 2 Q 2 Qirrev ∫1 T =S−∫1 T => Q=T⋅dS−Qirrev where Qirrev≥0 => dUp⋅dV=T⋅dS−Qirrev => Qirrev=−dU−p⋅dVT⋅dS ≥ 0 Which can also be written : Qirrev=−dHV⋅dpT⋅dS ≥ 0 This law is fundamental and explains the spontaneity of a thermodynamic process : the process will always go in the direction of “creating irreversibilities”. Some particular cases can be distinguished : 1. Isothermal, isochoric process : dU –T⋅dS=dAS⋅dT=dA≤0 The system will tend towards a reduction of the Helmoltz free energy. 2. Isobaric, isothermal process : dHT⋅dS=dGS⋅dT=dG≤0 The system will tend towards a reduction of the Gibbs free energy. 4.2 Liquids A liquid is considered as “ideal” if it is not compressible : dv≈0 In this case, the internal energy depends only on the temperature and ∂u=du=c ∂T dT On the other hand, the enthalpy now depends on the pressure : dh = c⋅dT v⋅dp and ds=dT T cv=cp=c In an isentropic liquid compression/expansion (ds = dT = 0), the enthalpy difference becomes: h=v⋅p 9PDF Image | An introduction to thermodynamics applied to Organic Rankine Cycles
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