Partial differentiation - Constants

[Jalo]

Homework Statement

Consider the following equality:

([itex]\frac{∂S}{∂V}[/itex])_T = ([itex]\frac{∂P}{∂T}[/itex])_V

If I rearrange the equality so that I write:

([itex]\frac{∂S}{∂P}[/itex])_? = ([itex]\frac{∂V}{∂T}[/itex])_?

What variables will be constant in each side?
I'm having some trouble in a few thermodynamics problems because of this...

Homework Equations

The Attempt at a Solution

I don't know how to do this. Normally I just ignore and assume that every variable except the variable of differentiation is a constant.
If anyone could confirm or correct me I'd be thankful.

Thanks.

 

[SammyS]

Homework Statement

Consider the following equality:

([itex]\frac{∂S}{∂V}[/itex])_T = ([itex]\frac{∂P}{∂T}[/itex])_V

If I rearrange the equality so that I write:

([itex]\frac{∂S}{∂P}[/itex])_? = ([itex]\frac{∂V}{∂T}[/itex])_?

What variables will be constant in each side?
I'm having some trouble in a few thermodynamics problems because of this...

Homework Equations

The Attempt at a Solution

I don't know how to do this. Normally I just ignore and assume that every variable except the variable of differentiation is a constant.
If anyone could confirm or correct me I'd be thankful.

Thanks.

The following may help you.

For the case in which three variables can be related by a function of the form f(x, y, z) = 0, then the following relations hold.

[itex]\displaystyle \left(\frac{\partial x}{\partial y}\right)_z\left(\frac{\partial y}{\partial z}\right)_x\left(\frac{\partial z}{\partial x}\right)_y = -1[/itex]

[itex]\displaystyle \left(\frac{\partial x}{\partial y}\right)_z = \frac{1}{\left(\frac{\partial y}{\partial x}\right)_y}[/itex]

See the following two Wikipedia entries:

http://en.wikipedia.org/wiki/Triple_product_rule

http://en.wikipedia.org/wiki/Exact_differential#Cyclic_relation