# Dimensional analysis involving partial derivatives

• I
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?

RPinPA
Homework Helper
The dimensions of dA/dB are A/B, for any two quantities A and B. You can see that from the definition of derivative.

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##

Wledig
Thanks, I wasn't sure about what to do with the ln. Got intimidated, I guess.