Fundamental definition of temperature

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kasse
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The fundamental definition of temperature is

[tex] T^{-1} = \frac{dS}{dE}[/tex]

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