Calc E as Fn of T for Ideal Paramagnet

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Homework Statement

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.

Homework Equations

[tex] \frac{1}{T}=\frac{\delta S}{\delta U}<br /> [\tex]<br /> <br /> <h2>The Attempt at a Solution</h2><br /> <br /> 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:<br /> <br /> [tex] \frac{1}{T}=\frac{\delta S}{\delta U}<br /> \frac{\delta S}{\delta U}=-2CE<br /> \frac{1}{T}=-2CE<br /> E=\frac{1}{-2CT}<br /> [\tex]<br /> <br /> In this case, the graph appears shaped like [tex]y=-\frac{1}{x} [\tex] dilated by $$\frac{1}{2C} [\tex]. <br /> <br /> I reasoned that in a paramagnet entropy will decrease as energy increases, so the system will more willingly give away energy, hence increasing the temperature.$$[/tex][/tex][/tex]

 

[relativespeak]

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.