Solved: "How to go from H = T S..." - Plainmath

kemecryncqe9

Answered question

2022-11-23

How to go from

H = T S + μ N

to

d H = T d S + V d P

Answer & Explanation

smeachtaczm

Beginner2022-11-24Added 14 answers

(1) Starting from

H = U + P V

, we have

d H = d (U + P V) = d U + P d V + V d P .

In conjunction with the fundamental relation

d U = T d S - P d V + μ d N

, we obtain

d H = T d S + V d P + μ d N .

(2) Starting from

H = T S + μ N

, we have

d H = d (T S + μ N) = T d S + S d T + μ d N + N d μ .

In conjunction with the Gibbs–Duhem relation

S d T - V d P + N d μ = 0

, we obtain

d H = T d S + V d P + μ d N .

Same result.

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