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Deduce the following relationships Da=Pdv-sdt Dg =tds +vdp

Deduce the following relationships
Da=Pdv-sdt 
Dg =tds +vdp 

Grade:12th pass

1 Answers

Arun
25750 Points
5 years ago
We have seen that the internal energy is
conserved and depends on mechanical (dw) and thermal (dq) energy. Given that pressure‐volume work done by the system is dw = ‐PdV and that the entropy change can be expressed as dS = dq/T (i.e. dq = TdS) we can express the internal energy as
dU = TdS – pdV
By a transformation of variables we define H = U + PV or dH = d(U+PV) = dU + PdV + VdP. Therefore,
dH = TdS + VdP

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