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

4

Explanation

Diffusion coefficient `prop` mean free pathxxmean speed
i.e., `D prop bar(l)xxbar(c )`
But `bar(l)=(1)/(sqrt(2)pisigma^(2))(RT)/(PN_(0))`
or `bar(l) prop (T)/(P)" and "bar(c )=sqrt((8RT)/(piM))`
or `bar(c ) prop sqrt((T)/(M))`
`:. D prop (T)/(P).sqrt((T)/(M)) " or " D prop (T^(3//2))/(Psqrt(M))`
`:. (D_(1))/(D_(2))=((T_(1))/(T_(2))^(3//2)(P_(2))/(P_(1))`
or `(D_(1))/(D_(2))=((T)/(4T))^(3//2)((2P)/(P))=((1)/(4))^(3//2)xx2`
`=((1)/(2))^(3)xx2=(1)/(4)`
or `D_(2)=4D_(1)`