# Which of the following is the best description of the relationship between average kinetic energy and measurable quantities of an ideal gas?

## A) It is directly proportional to temperature. B) It is dependent on only the pressure. C) It is related to the molar volume. D) It is not related to pressure.

Jul 3, 2017

It's an ideal gas, but we still have to consider the equipartition theorem for the high-temperature limit of the average translational kinetic energy:

$\boldsymbol{{K}_{t r , a v g} = \frac{3}{2} n R T}$, in units of $\text{J}$

where the $3$ was from the three cartesian degrees of freedom. $R = \text{8.314472 J/mol"cdot"K}$ and $T$ (i.e. temperature in $\text{K}$) are from the ideal gas law.

This tells us ${K}_{t r , a v g}$ explicitly depends on the mols of gas and the temperature it is at. Note that this is in units of $\text{J}$, not $\text{J/mol}$, so this is just the non-molar, average translational kinetic energy.

While it's true that the pressure is given by

$P = \frac{n R T}{V} = \frac{2}{3} \frac{{K}_{t r , a v g}}{V}$,

you should still find then that $\boldsymbol{A}$ is the best answer, being the most straightforwardly correct.

(There is a dependence on pressure, but it is NOT true that it is dependent on ONLY the pressure.)