Perfect gasses temperature vs kinetic energy per molecule

[madah12]

Homework Statement

I have been wondering about temperature and it's relation to kinetic energy I didn't study thermodynamics so I hope that replies could be simplified.I am trying to think about the perfect gas law to relate kinetic energy per molecule to temperature, and I want to know if I have a somewhat close understanding.

Homework Equations

PV=RnT

The Attempt at a Solution

PV=RnT
I am thinking that P*V expresses the energy stored in the gas molecules since P =F/A and V=m^3 so P*V=F*m which is the unit of work so W=RnT
and since the work expresses the change of kinetic energy
deltaK= RnT
(delta K)/n = RT
so this gives me the intuition that since the change of kinetic energy per molecule is equal to a constant times the temperature so its proportional to it. I didn't study thermodynamics and only basics of physical chemistry so probably there are things I missed but is my intuition at least correct?

 

[lightgrav]

Your intuition (or subconsciously-remembered info) is in the right direction
... but the PV is related to the Work that can be done on the Area (2-d),
not the entire molecule KE , which comes from motion in all 3 dimensions.
So, the KE per molecule (an average, of course) is actually 3/2 * PV/n .
... this is translational KE of the molecule's center-of-mass, not including
rotational KE and vibrational KE of the atoms relative to that c.o.m.

It is more traditional to write KE = 3/2 N kT , with N being the number of molecules,
and k is Boltzmann's konstant = 1.38E-23 J/K , which is R/N_avagadro .
The "3" signifies that there are 3 modes of motion which contribute to this KE ; every mode (including means rotations and vibrations also, if they occur) in a molecule holds E(average) = 1/2 kT .