Find ∂G/∂Na at T,p,Na'≠a | Thermodynamics Q

[mcdonkdik]

Find (∂G/∂N_a)_T,p,Na'≠a

of

G(T, p, x1, x2,...) = Ʃx_aπ_a(T) + RTƩx_aln(x_ap/p₀)

p.s. the sum is over all alpha. π(T) is some function of T:

so first i multiplied thru by Ntotal (N).. giving extensive G.. then differentiated this wrt Na.

My problem is how to differentiate the second part, i.e.

d/dNa = π_a(T) + d/dN_a(RTƩN_aln(N_aP/NP₀)

plssssssss help

mcdonkdik

 

[_coyote_]

2's answer:The second part can be differentiated by the chain rule. You have: d/dNa (RTƩNaln(NaP/NP0) = RT * ∂/∂Na (ƩNaln(NaP/NP0))Now replace the summation with a single term where a = Na'. This gives: d/dNa (RTƩNaln(NaP/NP0) = RT * ln(Na'P/NP0). Therefore, your final answer is: dG/dNa = πa(T) + RT ln(Na'P/NP0).