Comprehension-3
An ideal gas initially at pressure `p_(0)` undergoes a free expansion (expansion against vacuum under adiabatic conditions) until its volume is `3` times its initial volume. The gas is next adiabatically compressed back to its original volume. The pressure after compression is `3^(2//3)p_(0)`.
The gas, is monoatomic, is diatomic, is polyatomic, type is not possible to decide from the given information. What is the ratio of the average kinetic energy per molecule in the final state to that in the initial state?

Options

A. is monoatomic.
B. is diatomic
C. is polyatomic
D. type is not possible to decide from the given information.

Answer

A

Explanation

For adiabatic compression, initial conditions are `(p_(0))/(3)` and `3v_(0)`. Find volume and pressure are `v_(0)` and `3^(2//3) p_(0)`.
`(p_(0))/(3) (3v_(0))^(gamma) = 3^(2//3) p_(0)(v_(0))^(gamma) rArr 3^(gamma-1) = 3^(2//3)`
or `gamma -1 =(2)/(3) rArr gamma - (5)/(3)` i.e. gas is monoatomic