# Dimensional analysis involving partial derivatives

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## Main Question or Discussion Point

It is mentioned in Reif's book, statistical physics, that trough dimensional analysis it can be shown that: $$\frac{1}{\beta} = kT$$ where $\beta$ equals $\frac{\partial \ln \Omega}{\partial E}$ and k is the Boltzmann constant. I don't quite see how to reach this result, can anyone give me a hand here?

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RPinPA
The log is dimensionless (arguments of logs, exponentials, trig functions should always be dimensionless). So the units of $\partial{ln (\Omega)}/\partial{E}$ are 1/energy.
Therefore the units of $1/\beta$ are energy, and those are the dimensions of $kT$