Physical Chemistry Third Edition

162 4 The Thermodynamics of Real Systems

We now obtain some additional useful equations. Equations (4.1-8) and (4.2-3) give

dA−SdT−PdV (closed system) (4.2-15)

so that

(

∂A

∂T

)

V,n

−S (4.2-16)

(

∂A

∂V

)

T,n

−P (4.2-17)

A third Maxwell relation is

(

∂S

∂V

)

T,n



(

∂P

∂T

)

V,n

(a Maxwell relation) (4.2-18)

Equations (4.1-13) and (4.2-3) give

dG−SdT+VdP (closed system) (4.2-19)

so that

(

∂G

∂T

)

P,n

−S (4.2-20)

(

∂G

∂P

)

T,n

V (4.2-21)

Our fourth Maxwell relation is

(

∂S

∂P

)

T,n

−

(

∂V

∂T

)

P,n

(a Maxwell relation) (4.2-22)

A mnemonic device for writing the Maxwell relations is to write a blank relation

(

∂···

∂···

)

···,n



(

∂···

∂···

)

···,n

and then to putPandVin opposite corners andTandSin the other opposite corners.

There are four ways to do this, giving the four Maxwell relations. In each relation the

independent variable in one derivative is held constant in the other derivative andn

is fixed in both of the derivatives. IfTandVoccur in the same derivative, attach a

negative sign to one side. Otherwise, the signs are positive.