The volume of a diatomic gas `(gamma = 7//5)` is increased two times in a polytropic process with molar heat capacity ` C = R`. How many times will the rate of collision of molecules against the wall of the vessel be reduced as a result of this process?

Answer

B, C, D

Explanation

In the process `p V^x = constant C = (R )/(gamma - 1) + (R )/(1 - x)`,
Given, `C = R and gamma = 7//5`
Substituting these values, we get `x = (5)/(3)`
Now, `PV^(5//3) = "constant or" p prop (1)/((V)^(5//3))`
By increasing volume to two times pressure will decrease `(2)6(5//3)` times.
`v_(r m s) prop sqrt(T) "or "v_(r m s) prop sqrt(p V)`
or `v_(r m s) "will become" sqrt((2))/(2)^(5//3)` times
or `v_(r m s) "will become" (2)^(-1//3)` times
or `(1)/((2)^(1//3)` times
Now, `p prop ("no. of collisions") (v_(r m s)`
`(1)/((2)^(5//3) prop ("no. of collisions") (1)/((2)^(1//3)`
or number of collisions will decrease `(2)^(4//3)` times.