- #1
curio_city
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Homework Statement
[tex] \frac{dq}{dT}=\sum_{i} g_i \frac{dq}{dT} e^{-\frac{ε_i}{kT}} = \frac{1}{kT^2}\sum_{i} g_i ε_i e^{-\frac{ε_i}{kT}} = \frac{1}{kT^2} \bar{ε} q[/tex]
Homework Equations
[tex]q=\sum_{i} e^{-\frac{ε_i}{kT}}[/tex] or for degenerate states, [tex]q=\sum_{I} g_i e^{-\frac{ε_I}{kT}}[/tex]
The Attempt at a Solution
The equations in (1) are just set out in my notes. My problem is understanding the last step: I take [itex]\bar{ε}[/itex] to be the average molecular energy, since later they show that [itex]\bar{ε}_{trans}=\frac{3}{2}kT[/itex].
How can [itex]\sum_{i} g_i ε_i [/itex] be the mean, without dividing by N? Isn't it the total molecular energy?