# 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.

##### 1 Answer

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 **mols** of gas and the **temperature** it is at. Note that this is in units of

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

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