Relationship between pressure and temperature (derivation, kinetic theory of gases)

In this video, I derive the relationship between pressure and temperature using the kinetic theory of gases. We will see the relationship between the temperature and the mean kinetic energy of the gas molecules. Furthermore, we will show that the pressure depends only on the energy density in the gas.

00:00 ideal gas
01:19 cause of the pressure at the microscopic level
02:38 parameters influencing the gas pressure
03:43 collision volume
06:38 momentum transfer (impulse)
08:44 gas as a continuum
10:55 mean of the speed squares
12:22 kinematic approach
13:58 energetic approach
16:01 microscopic interpretation of temperature
16:52 internal energy density

[konstantinos_chatzigrigorakis]

Perfect analysis. Thank you very very much.

[michaeltamajong]

"But now comes a crucial point. If we consider the gas as a kind of coherent mass, a so called continuum, then within the time period dt, the total number of molecules Nx in the collision volume would have changed their momentum exactly once each by the given amount. Thus, if we consider the total impulse of all molecules in the collision volume and therefore the total force these molecules exert on the piston, then both times are indeed identical." I have no idea what that means and how that conclusion is made.