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## Homework Statement

A molecule has 4 states of energy -1, 0,0 and 1. Find its partition function and limit of energy as T → ∞.

## Homework Equations

## The Attempt at a Solution

[tex]Z = \sum_r e^{-\beta E} = e^{-\beta} + 2 + e^{\beta}[/tex]

[tex]U = -\frac{\partial ln(Z)}{\partial \beta} = \frac{e^{-\beta} - e^{\beta}}{e^{-\beta} + 2 + e^{\beta}}[/tex]

As ##T→\infty##, ##exp(-\beta) \approx 1 - \beta## and ##exp(\beta) \approx 1 + \beta##.

Thus,

[tex]U \approx \frac{(1-\beta) - (1+\beta)}{2 + (1+\beta) + (1-\beta)} = -\frac{\beta}{2} = -\frac{1}{2kT}[/tex]

The equipartition theorem should take over with Energy = 4 * (1/2)kT = 2kT = 2/β.

But instead i'm getting -β/2.