# We say that Temperature is basically average kinetic energy so can't we say that unit of temperature is Joules??

May 12, 2017

No, we don't. We say that temperature is PROPORTIONAL to the average kinetic energy...

${K}_{a v g} \propto T$

More explicitly, from the so-called equipartition theorem,

${K}_{a v g} = \frac{N}{2} n R T$,

where $N$ is the number of degrees of freedom (unitless), $n$ is the number of $\text{mol}$s of gas, and $R$ is the universal gas constant.

When $R$ has units of $\text{J/mol"cdot"K}$ and $T$ has units of $\text{K}$... the units of kinetic energy are therefore

cancel"mols" xx "J/"cancel"mol"cdotcancel"K" xx cancel"K" = color(blue)("J")

even though we continue forevermore to use units of $\text{K}$ for absolute temperature.