Question
Asked Oct 6, 2019
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This problem is (8.4) from a book  "Thermodynamics and Statistical Mechanics An Integrated Approach by M. Scott Shell"

8.4. Rigorously show that (aV/oN)T,P of Eqn. (8.7) is equal to V/N.
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8.4. Rigorously show that (aV/oN)T,P of Eqn. (8.7) is equal to V/N.

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(8.7)
aNT,P
ОР/ т,N
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(8.7) aNT,P ОР/ т,N

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Expert Answer

Step 1

The change in Gibb’s free energy for a reversible process is given by equation (1). At, constant temperature, equation (1) reduces to equation (2) as dT is equated to zero. Equation (2) can rearranged and written as equation (3).

 

(1)
(2)
dG=V . (3)
dG VdP-SdT ...
dG VdP
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(1) (2) dG=V . (3) dG VdP-SdT ... dG VdP

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Step 2

On differentiating equation (3) with respect to number of moles of component i, equation (4) is obtained where Vi bar is partial molar volume or V/N of component i. Equation (4) is rewritten as equation (5) on rearrangement. It is known that the partial change in Gibb’s free energy with respect to the moles of component i at constant T a...

д (dG
дn, dP т.N
(4)
dOG
V.
-и
аP дn, т.N
(5)
!
(6)
ЕM
дn; т.N
(ди
(7)
ОР
Т.N
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д (dG дn, dP т.N (4) dOG V. -и аP дn, т.N (5) ! (6) ЕM дn; т.N (ди (7) ОР Т.N

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