- #1

relativespeak

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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}

[\tex]

## 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.

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