The root mean square speed of an ideal gas is given by : `u_("rms") = sqrt((3RT)/M)` Thus we conclude that `u_("rms")` speed of the ideal gas molecules is proportional to square root of the temperature and inversely proportional to the square root of the molar mass. The translational kinetic energy per mole can also be given as `1/2Mu_(rms)^(2)` . The mean free path (`lambda`) is the average of distances travelled by molecules in between two successive collisions whereas collision frequency (C.F.) is expressed as number of collisions taking place in unit time. The two terms `lambda` and C.F. are related by : `C.F = (u_("rms")/lambda)`
Which of the following relation is correct for an ideal gas regarding its pressure (P) and translational kinetic energy per unit volume (E) ?

Options

A. `P = 2/3  E `
B. `P = 3/2E`
C. `P=1/2E`
D. `P = 2E`

Explanation

`PV = 1/3 MC^2 , KE = 1/2 MC^2 implies MC^2 = 2KE `
`implies PV = 1/3 xx 2KE , (KE)/(V) = E implies P = 2/3 E`