increases then pressure will increase. For example when we pump air inside the cycle tyre or car tyre essentially the number density increases and as a result the pressure increases. (ii) Mass of the molecule Since the pressure arises due to momentum transfer to the wall, larger mass will have larger momentum for a fixed speed. As a result the pressure will increase.
(iii) Mean square speed For a fixed mass if we increase the speed, the average speed will also increase. As a result the pressure will increase. For simplicity the cubical container is taken into consideration. The above result is true for any shape of the container as the area A does not appear in the final expression ( .
). Hence the pressure exerted by gas - - - - Unit Kinetic theory of gases U RT = µ Since Nk = μR . Here μ is number of moles. Gas constant R = .
J molk Temperature T = + =300K U = × . × . × = . J This is approximately equivalent to the kinetic energy of a man of kg running with a speed of m s - .
. . Relation between pressure and mean kinetic energy From earlier section, the internal energy of the gas is given by U NkT = The above equation can also be written as U = PV since PV = NkT P = U u ( . ) From the equation ( .
), we can state that the pressure of the gas is equal to two thirds of internal energy per unit volume or internal energy density ( u = U V ). Writing pressure in terms of mean kinetic energy density using equation ( . ) nmv ρ ( . ) where ρ = nm = mass density (Note n is number density) Multiply and divide R.H.S of equation ( .
) by , we get ρ ( . ) KE = (i) The average kinetic energy of the molecule is directly proportional to absolute temperature of the