10.3 Solutions
451
Work (W ) is energy that is transferred from one body to another body
due to a force that acts between them.
The function, G = U + PV −T S, is known as Gibb’s function or Gibb’s
energy.
Relations:
(i) Enthalpy
H = U + PV
(1)
dH = dU + PdV + V dP = T ds + V d p
(2)
∵
T ds = dU + PdV
(3)
It follows that enthalpy is a function of entropy (S) and pressure
(P).
∴ H = f (S, P)
dH =
∂ H
∂ S
P
dS +
∂ H
∂ P
S
dP
(4)
Comparing (4) with (2)
∂ H
∂ S
P
= T and
∂ H
∂ P
S
= V
(5)
(ii) Gibb’s function:
G = U + PV − T S
(6)
dG = dU + PdV + V dP − T dS − SdT
But
T dS = dU + PdV
∴ dG = V dP − SdT
(7)
Thus G is a function of two independent variables P and T .
G = f (P, T )
dG =
∂G
∂ P
T
dP +
∂G
∂ T
P
dT
(8)
Comparing (8) with (7)
∂G
∂ P
T
= V
(9)
∂G
∂ P
P
= −S
(10)