Question

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

Answer 1

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

`K_(avg) prop T`

More explicitly, from the so-called equipartition theorem,

`K_(avg) = N/2nRT`,

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

When `R` has units of `"J/mol"cdot"K"` and `T` has units of `"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.