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First Law and Second Law Combined

From 1st law we get   dQ = dU + PdV

From 2nd law we get   dQrev = TdS

:.       Combining 1st & 2nd law

Again for enthalpy

TdS= dU +PdV

H=U+PV

dH = dU + PdV + V dP

= TdS+ VdP

TdS = dH- VdP