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1. Homework Statement

1. Homework Statement

Starting with the first Maxwell relation, derive the remaining three by using only the relations:

$$\left(\frac{\partial x}{\partial y}\right) _{z} \left(\frac{\partial y}{\partial z}\right) _{x} \left(\frac{\partial z}{\partial x}\right) _{y} = -1$$

and

$$\left(\frac{\partial x}{\partial y}\right) _{f} \left(\frac{\partial y}{\partial z}\right) _{f} \left(\frac{\partial z}{\partial x}\right) _{f} = 1$$

## Homework Equations

The Maxwell relations are:

$$\left(\frac{\partial T}{\partial V}\right) _{S} = - \left(\frac{\partial P}{\partial S}\right) _{V}$$

$$\left(\frac{\partial T}{\partial P}\right) _{S} = \left(\frac{\partial V}{\partial S}\right) _{P}$$

$$\left(\frac{\partial S}{\partial V}\right) _{T} = \left(\frac{\partial P}{\partial T}\right) _{V}$$

$$\left(\frac{\partial S}{\partial P}\right) _{T} = - \left(\frac{\partial V}{\partial T}\right) _{P}$$

## The Attempt at a Solution

My problem is, that I don't understand the second relation they give me to solve the problem. I'm not quite sure what would be f in this relation. I mean, in the book they define it as a function of x, y, and z, but I can't really use it. I don't know where to start. I'm sure that the problem is quite easy, but I need a little push to get started.

Any help would be appreciated