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Comprehension-2 A mono atomic ideal gas...

Comprehension-2
A mono atomic ideal gas is filled in a non conducting container. The gas can be compressed by a movable non conducting piston. The gas is compressed slowly to `12.5%` of its initial volume.
The percentage increases in the temperature of the gas is

A

`400%`

B

`300%`

C

`-87.5%`

D

`0%`

Text Solution

Verified by Experts

The correct Answer is:
B
Let initial temperature and volume be `T_(0)` and `V_(0)`. Since the process is adiabatic, the final temperature and volume is `TV^(gamma-1) = T_(0)V_(0)^(gamma-1) (gamma = (5)/(3)` for mono atomic gas)
`T = T_(0) ((V_(0))/(V_(0)//8))^((2)/(3)) = 4T_(0)`
`:.` percentage increaase in temperature of gas is
`(DeltaT)/(T_(0)) xx 100 = (3T_(0))/(T_(0)) xx 100 = 300%`
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