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
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.)