# Homework Help: Entropy of an ideal paramagnet

1. Mar 22, 2007

### PeterPoPS

1. The problem statement, all variables and given/known data
The entropy of an ideal paramagnet is given by

$$S = S_0 - CU^2$$

where U is the energy, which can be positive or negative, and C is a positive constant. Determine the equation for U as a funtion of T and sketch your result.

2. Relevant equations

$$\frac{1}{T} = \left(\frac{\partial S}{\partial U}\right)_V$$

3. The attempt at a solution
I differentiated the given equation, treating S0 as not depending on U.

$$\frac{1}{T} = -2CU$$

$$U(T) = -\frac{1}{2CT}$$

so far so good i hope. But in the question it says U can be positive or negative.. But in my last equation the only way of getting U positive is by having a negative temperature??
Or should I just answer that the energy is strict negative in this case?

Any help will do!