The process by which a gas 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:
`(dp)/(dt)=(kT)/(V)((dN)/(dt))`
where Rate of change of number of molecules
`rArr" "-(dN)/(dt)=(pA_(0))/((2pimkR)^(1//2))`
where, k= Boltzmann constant
`N_(A) = `Avogadro's number
`T=` temperature (in K) `rArr" "-(dN)/(dt)=(pA_(0))/((2pimkR)^(1//2))`
`N_(A) = `Avogadro's number
`T=`temperature (in K)
`V=`volume of vessel
`N=1` no.of molecules
`A_(0)=` area of aperture
`m=`mass of single molecule
`gamma=(V)/(A_(0))sqrt((2pim)/(kT))`
If initial pressure is `P_(0)` then pressure of gas at any time t in the container at constant V and T is given by:

Options

A. `P_(0)e^(-t//y)`
B. `P_(0)e^(t//gamma)`
C. `P_(0)(1-e^(-t//gamma))`
D. `P_(0)(1-e^(t//gamma))`

Answer

A