Pressure of Ideal Gas

The force experienced per unit area by the walls of the container, due to continuous collision of gas molecules with the walls and the transfer of momentum during each collision, is called the pressure exerted by the gas.

P = \[\frac {1}{3}\].\[\frac {mN}{V}\].\[\overline {V^2}\]

where:

• m = mass of one molecule
• N = total number of molecules
• V = volume of the gas
• \[\overline {v^2}\] = mean square speed of the molecules

• Pressure of an ideal gas = ⅔ of mean kinetic energy of translation per unit volume.
• At constant V and T: p ∝ mN — more mass → more molecules → more collisions → higher pressure.
• At constant m and T: p ∝ \[\frac {1}{V}\] — less volume → molecules closer → more collisions → higher pressure.
• At constant m and V: p ∝ T — higher temperature → faster molecules → greater momentum → higher pressure.