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

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

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Answer 1 · 2017-05-12T07:39:26

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

$K_{a v g} \propto T$ $K_(avg) prop T$

More explicitly, from the so-called equipartition theorem,

$K_{a v g} = \frac{N}{2} n R T$ $K_(avg) = N/2nRT$ ,

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

When $R$ $R$ has units of $J/mol \cdot K$ $"J/mol"cdot"K"$ and $T$ $T$ has units of $K$ $"K"$ ... 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 $"K"$ for absolute temperature.

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

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