Which of the following thermodynamic relation is correct?

Options

A. `dG =V d p -SdT`
B. `dE = P dV + T dS`
C. `dH = - V dP +T d S`
D. `Dg= vDp+ S dT`

Answer

a

Explanation

`G= H - TS ` But `H =U + PV`
`:. G= U + PV - TS`
Differentiating it completely ,we get
`dG=dU +PdV+ VdP - TdS - SdT` …(i)
But `dU =dq+dw` and `w= -PdV`
`:. dU = d-PdV` or `dq = dU+ PdV` …(ii)
Further, for averversible process, `dS= ( dq)/(T)`
or `dq=TdS` ....(iii)
From (ii) and (iii), `dU +PdV=T DeltaS`
Substituting this in (i),weget`dG =VdP - SdT`