Physical Chemistry , 1st ed.

Other relationships can be derived from the other natural variable equa-

tions. From dH:



H

S



p

T (4.20)



H

p



S

V (4.21)

From dA:



A

T



V

S (4.22)



V

A



T

p (4.23)

and from dG:



G

T



p

S (4.24)



G

p



T

V (4.25)

If we know that Gis a function ofpand T, and we know how Gvaries with p

and T, we also know Sand V. Also, knowing Gand how it varies with pand

T, we can determine the other state functions. Since

HU pV

and

GHTS

we can combine the two equations to get

UG TSpV

Substituting from the partial derivatives in terms ofG(that is, equations 4.24

and 4.25), we see that

UGT

G

T



p

p

G

p



T

The differential form of this equation is

dUdG^

G

T



p

dT^

G

p



T

dp (4.26)

We already know dG, and by knowing the two partial derivatives, we can de-

termine Uas a function ofTand p. Expressions for the other energy state func-

tions can also be determined. The point is, if we know the values for the proper

changes in one energy state function, we can use all of the equations of ther-

modynamics to determine the other changes in energy state functions.

Example 4.5

What is the expression for H, assuming one knows the behavior ofG(that is,

the partial derivatives in equations 4.24 and 4.25)?

Solution

We can use the equation

GHTS

98 CHAPTER 4 Free Energy and Chemical Potential