Hello there,

I am currently working on a question I am having problems with. I tried to solve it, but to no avail; it states that this expression is always valid for any three-variable dependent function:

(picture 1)

It states that I need to prove that by considering the done volume work while doing a reversible compression on an ideal gas, expressed by:

(picture 2)

and we set (x,y,z)=(p,V,T). The last derivative can be solved by using the ideal gas law.

Honestly, I don't know where to start. I don't understand how I should put up the differentials, because I don't see how w is dependent on p, the only thing that I thought of would be that the work is defined as -pdV, but I would not know how to work with the dV on itself that would be left.

I know that those are all partial derivatives and that the variable on the outside of the bracket is kept constant and that I need to formulate the function in such a way that both variables in the derivative expression appear on the right side, but I don't know the way to combine all three needed parameters. Any help would really be appreciated.