Modern Thermodynamics
- Chapter 1
43
The same is valid for all higher derivatives such as
∂3U
∂T2∂V
, i.e. the order of differentiation does not
matter.
Basic Identities
Consider three variables x, y and z, each of which can be expressed as a function of the other two
variables, x=x(y,z), y=y(z,x) and z=z(x,y). (p,V and T in the ideal gas equation pV=NRT is an example).
Then the following identities are valid:
∂x
∂yz



=
1
∂y
∂xz


(A1.1.6)
∂x
∂yz



∂y
∂z


x
∂z
∂xy



= −1
(A1.1.7)
Consider a functions of x and y, f=f(x,y), other than z. Then:
∂f
∂xz



=
∂f
∂xy



+
∂f
∂yx∂xz




∂y
(A1.1.8)
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