In an educational video on derivation of the formula (3/2)PV=Kinetic energy of the gas, it was assumed that 1/3 of the particles are linearly translating along the three axes of the coordinate plane in the cubic container and there are N particles where P and V are the pressure exerted and volume of the gas, the pressure due to each particle of the gas on a wall was calculated as (mv^2)/x m is the mass of the particle, v is it’s velocity and x is the length of the cubic container, This when divided by area of one wall (x^2) gave the pressure exerted by one particle,p as (mv^2)/V this was then multiplied by N/3 to give the total pressure exerted on one of the wall(which is the total pressure of the wall), thereon the above formula is derived.
However my doubt is, how do we apply the assumption(emboldened assumption) to the general case for the gas’ pressure, since it’s applicable only if the N/3 particles are simultaneously hitting the wall at every instant, but even in this case it might be that only some are hitting the wall while others aren’t and still reaching the wall, and the distribution is uneven maybe 3 particles hit at one instant and 300 at another so how do we get the pressure all the time?
Further this reasoning can be extended to say that there will actually be no constancy in pressure ever, so how is it even a state function macro state? It should be impossible for a constant pressure to exist, be it an ideal or real gas. And assuming that it can be-taking an average pressure-how is one to find it out, and how can we use such a highly fluctuating quantity(even in equilibrium) in practice? Also it should be not possible to get a constant reading on a barometer, which however is not the case!
How do we solve this query?