# Calculate E as a function of T using the given fn of entropy for an ideal paramagnet

1. Feb 4, 2013

### relativespeak

1. The problem statement, all variables and given/known data

The entropy of an ideal paramagnet is given by S=S_{0}+CE^{2}, where E is the energy (which can be positive or negative) and C is a positive constant. Determine the equation for E as a function of T and sketch your result.

2. Relevant equations

[tex]
\frac{1}{T}=\frac{\delta S}{\delta U}
[\tex]

3. The attempt at a solution

I'm fairly certain I solved correctly, but the solution seems to simple. I confused about whether the E here is the same as the U in the partial derivative equation above, in which case:

[tex]
\frac{1}{T}=\frac{\delta S}{\delta U}
\frac{\delta S}{\delta U}=-2CE
\frac{1}{T}=-2CE
E=\frac{1}{-2CT}
[\tex]

In this case, the graph appears shaped like [tex] y=-\frac{1}{x} [\tex] dilated by [tex] \frac{1}{2C} [\tex].

I reasoned that in a paramagnet entropy will decrease as energy increases, so the system will more willingly give away energy, hence increasing the temperature.

Last edited: Feb 4, 2013
2. Feb 4, 2013

### relativespeak

Re: Calculate E as a function of T using the given fn of entropy for an ideal paramag

Can someone tell me what I'm doing wrong with LaTex? I'm new to it and don't understand the problem with my code.