How to explain the dependence of the ideal gas pressure on the vessel wall on the mean square of the molecular velocity?

The higher the velocity of the molecules, the greater the number of molecules per unit time will have time to collide with the wall and the greater the pressure will be created. In addition, since the force acting on the wall from the side of the particle increases, when it hits the wall, the particle with a higher velocity receives a greater acceleration: which again leads to an increase in pressure. Combining these two conclusions, we find that the gas pressure on the wall increases in proportion to the average value of the square of the velocity or the average kinetic energy of the molecules.

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