`400 c c` volume of gas having `gamma=5/2` is suddenly compressed to `100 c c`. If the initial pressure is `P`, the final pressure will be

Options

A. `P//32`
B. `8P`
C. `32P`
D. `16P`

Answer

C

Explanation

Here `V_(1)=400"cc",V_(2)=100"cc",gamma=5/2`
Sudden compression is an adiabatic process.
For an adiabatic process ,
`PV^(gamma)=` constant
As `P_(2)V_(2)^(gamma)=P_(1)V_(1)^(gamma)`
or `P_(2)P_(1)((v_(1))/(v_(2)))^(gamma)=P(400/100)^(5//2)=P`
`xx4xx4sqrt(4)=32P`