2.What are all of the Maxwell relations for the differential expression of Gibbs Freeenergy of dG s-SdT + Vdp +udn, ?

Given:dG ≤ -sdT + VdP + ∑μidni12Asked:To find all the Maxwell's equations.The given differential equation can be safely writtena sdG ≤ -SdT + VdP + μdn ...(1)(this makes the whole equation more general and in complete differential form)Now we know that , if there is a function F(x,y), thendF = ∂F∂xdx + ∂F∂y dySimiarlt here we have G(T, P, n)therefore dG ≤ ∂G∂TP,ndT + ∂G∂PT,ndP + ∂G∂nP,Tdn ...(2)Now comparing (1) and (2)∂G∂TP,n = -S ...(A)∂G∂PT,n = V ...(B)∂G∂nP,T = μ ...(C)Now also one of the property of differential is that ∂2F∂x∂y = ∂2F∂y∂xSimilarly for G we get 3 equations∂2G∂P∂T = ∂2G∂T∂P ...(3)∂2G∂n∂T = ∂2G∂T∂n ....(4)∂2G∂n∂P = ∂2G∂P∂n ...(5)these double differentials can be separated as well as shown belowFor (3)∂∂PT,n ∂G∂TP,n = ∂∂TP,n ∂G∂PT,n from (A) and (B)∂∂PT,n (-S) = ∂∂PT,n Vtherefore-(∂S∂P)T,n = (∂V∂P)T,n ....(6)Similarly (4) can be written as∂∂nP,T ∂G∂TP,n = ∂∂TP,n ∂G∂nP,Tfrom (A) and (C)∂∂PT,n (-S) = ∂∂TP,n(μ)therefore-(∂ S∂P)T,n = (∂ μ∂T)P,n ....(7)Similarly (5) can be written as∂∂nP,T ∂G∂PT,n = ∂∂PT,n ∂G∂nP,Tfrom (B) and (C)∂∂nP,T (V) = ∂∂PT,n (μ) therefore(∂V∂n)P,T = (∂ μ∂P)T,n ....(8)Therefore the derived Maxwell's relations are equation number (6), (7), and (8)

Answered: What are all of the Maxwell relations…

What are all of the Maxwell relations for the differential expression of Gibbs Free energy of dG s-SdT + Vdp + £udn, ?