Question

The rate of change of pressure (p) of a gas at constant temperature and constant external pressure due to effusion of gas from a vessel of constant volume is related to rate of change of number of molecules present by $\frac{dp}{dt}$=$\frac{kT}{V}$ $\frac{dN}{dt}$ where k=Boltzmann constant,T=temperature,V=volume of vessel and N =No of molecules and $\frac{dN}{dt}$=$\frac{-p{A}_0}{(2\pi mkT{)}^{1/2}}$, where $A_0$= area of office and m =mass of molecule.

The correct statement (s) is /are:

(I) Pressure will not fall to zero in infinite time.
(II) The time required for the pressure to decrease to half its initial value is independent of initial pressure.
(III) The relations given above are true for real gases also.

• A. I
• B. II
• C. III
• D. I and III

Answer 1

The correct option is C III

The correct statement (s) is /are
(I) Pressure will fall to zero in infinite time as the entire gas will effuse out.
(II) Time required for pressure to decrease to half its initial value is dependent of initial pressure.
When the initial pressure is high, the time required for pressure to decrease to half its initial value will be less and vice versa.
(III) The relations given above are true for real gases also.
Thus, only option III is correct. Options I and II are incorrect.