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Comprehension-3 An ideal gas initially...

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

A

is monoatomic.

B

is diatomic

C

is polyatomic

D

type is not possible to decide from the given information.

Text Solution

Verified by Experts

The correct Answer is:
A
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
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