PHYSICAL CHEMISTRY IN BRIEF

CHAP. 3: FUNDAMENTALS OF THERMODYNAMICS [CONTENTS] 86

In the same way,H=f(S, p) may be converted toH=f(T, p). By combining equations (3.34)
and (3.50) we arrive at

dH=CpdT+



V−T

(

∂V

∂T

)

p



dp. (3.52)

According to (3.25), the total differential of the functionU=f(T, V) is equal to the expression

dU=

(

∂U

∂T

)

V

dT+

(

∂U

∂V

)

T

dV. (3.53)

By comparing (3.51) and (3.53) we get

(

∂U

∂T

)

V

= CV, (3.54)

(

∂U

∂V

)

T

= T

(

∂p

∂T

)

V

−p. (3.55)

Note:The derivative of internal energy with respect to volume is called cohesive pressure.

Similarly we obtain the respective partial derivatives of the dependenceH=f(T, p)

(

∂H

∂T

)

p

= Cp, (3.56)

(

∂H

∂p

)

T

=− T+V

(

∂V

∂T

)

p

. (3.57)

Example

Prove that the internal energy of an ideal gas is only a function of temperature, i.e. that at a

fixed temperature it depends neither on volume nor on pressure.