`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 c c, V_(2)= 100 c c, gamma=5/2, P_(1)=P`
`P_(2)=?` for adiabatic change,
`P_(2)V_(2)^(gamma)=P_(1)V_(1)^(gamma)`
`:. P_(2)=P_(1)((V_(1))/(V_(2)))^(gamma)`
`P_(2)=P ((400)/(100))^(5//2)`
`= Pxx4xx4xxsqrt(4)=32P`