Question

The diffusion coefficient of an ideal gas is proportional to its mean free path and mean speed. The absolute temperature of an ideal gas is increased 4 times and its pressure is increased 2 times.As a result, the diffusion coefficient of this gas increases x times. The value of x is

Answer 1

Correct Answer - 4
Mean free path `(l) prop (T)/(P)`
Mean speed `(C _(av)) prop sqrt(T)`
Diffusion coefficient (D) is proportional to both mean free path (l) and mean speed
`:. D prop (T^(3//2))/(P)` .....(i)
If `T_(1)` is increased 4 times and `P_(1)` is increased 2 times
`D_(2) =(K(4T_(1))^(3//2))/(2P_(1))` ....(ii)
`(D_(2))/(D_(1))=((4)^(3//2))/(2)=(2^(2))/(2)=4`