Pressure of an ideal gas based on Kinetic theory
Elastic collision of a gas molecule with the wall of the container
Justifying the assumptions:-
- We have assumed the container containing the gas is a cube. The shape of the container is immaterial.
- For a vessel of any arbitrary shape, we can choose a small infinitesimal (planar) area and can prove the above derivation.
- We will see A and Δt are not there in the final result.
- By Pascal’s law pressure in one portion of gas in equilibrium is the same as anywhere else.
- All collisions are neglected.
- The number of molecules hitting the wall in time Δt was found to be ½ n AvxΔt, with random collisionsand asteady state of gas.
- Thus, if a molecule with velocity (vx, vy,vz)acquires a different velocity due to collision withsome molecules, there will always be some othermolecule with a different initial velocity whichafter a collision acquires the velocity (vx, vy, vz).
- Molecular collision, when they are not too frequent and the time spent in collision is very small compared to the time between collisions, will not have any affect in the above calculation.