Question

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.

Answer 1

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:

`bb(K_(tr,avg) = 3/2 nRT)`, in units of `"J"`

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

This tells us `K_(tr,avg)` explicitly depends on the mols of gas and the temperature it is at. Note that this is in units of `"J"`, not `"J/mol"`, so this is just the non-molar, average translational kinetic energy.

While it's true that the pressure is given by

`P = (nRT)/V = 2/3 (K_(tr,avg))/V`,

you should still find then that `bbA` 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.)