Fundamental definition of temperature

[kasse]

The fundamental definition of temperature is

<br /> T^{-1} = \frac{dS}{dE}<br />

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

 

[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.