# Fundamental definition of temperature

1. Jan 30, 2009

### kasse

The fundamental definition of temperature is

$$T^{-1} = \frac{dS}{dE}$$

How can I verify that the dimensions work in this equation?

Last edited: Jan 30, 2009
2. Jan 30, 2009

### jambaugh

Units of S over units of E = reciprocal of units of temperature.

Typically (in statistical mechanics calculations) S is a unitless number multiplied by Boltzmann's constant so it's kind of automatic given the units of Boltzmann's constant.