Chemistry - Ideal Gas Question with Solution | TestHub

The process by which a gas passes through a small hole into vacuum is called effusion. The rate of change of pressure (p) of a gas at constant temperature due to effusion of gas from a vessel of constant volume can be related to rate of change of number of molecules by the expression :     

$\frac{dp}{\mathrm{d}t}=\frac{kT}{V}\left(\frac{dN}{\mathrm{d}t}\right)$

where  Rate of change of number of molecules ⇒$-\frac{dN}{\mathrm{d}t}=\frac{p{A}_0}{{\left(2\pi mkT\right)}^{\frac{1}{2}}}$

 where        k = Boltzmann constant                       

N_A = Avogadro’s number                       

T = temperature (in K)                      

V = volume of vessel                          

N = No.of molecules                      

A₀ = area of aperture                          

m = mass of single molecule

$\gamma =\frac{V}{A_0}\sqrt{\frac{2\pi m}{kT}}$