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## Main Question or Discussion Point

In thermodynamics, we always need to use exact differential relations to find the so called Maxwell relations. For a function of x and y, z=z(x,y)

if dz = M(x,y)dx + N(x, y)dy

the complete conditon for above equation to be hold is

[tex]\frac{\partial M}{\partial y} = \frac{\partial N}{\partial x}[/tex]

Now, let see one of the relation on Helmholtz free energy

[tex]dF = -SdT - PdV[/tex]

apply the condition mentioned above, we get

[tex]\left(\frac{\partial P}{\partial T}\right)_V = \left(\frac{\partial S}{\partial V}\right)_T[/tex]

Well, in many materials (including some textbooks), they like to write it

[tex]\left ( {\partial T\over \partial p} \right )_{V,N} = \left ( {\partial V\over \partial S} \right )_{T,N}[/tex]

I don't know why they like to inverse those relation! What interesting is only this relations I found to be in reverse order, the others Maxwells relations are just fine!

if dz = M(x,y)dx + N(x, y)dy

the complete conditon for above equation to be hold is

[tex]\frac{\partial M}{\partial y} = \frac{\partial N}{\partial x}[/tex]

Now, let see one of the relation on Helmholtz free energy

[tex]dF = -SdT - PdV[/tex]

apply the condition mentioned above, we get

[tex]\left(\frac{\partial P}{\partial T}\right)_V = \left(\frac{\partial S}{\partial V}\right)_T[/tex]

Well, in many materials (including some textbooks), they like to write it

[tex]\left ( {\partial T\over \partial p} \right )_{V,N} = \left ( {\partial V\over \partial S} \right )_{T,N}[/tex]

I don't know why they like to inverse those relation! What interesting is only this relations I found to be in reverse order, the others Maxwells relations are just fine!