A diatomic gas at pressure P, compressed adiabatically to half of its volume, what is the final pressure-

Options

A. `(2)^(1.4)P`
B. `P//(2)^(1.4)`
C. `(2)^(5/3)P`
D. `P//(2)^(5//3)`

Answer

A

Explanation

For adiabatic conditions, `PV^(gamma)`=cosntant
`P_(1)V_(1)^(gamma)=P_(2)V_(2)^(gamma),V_(2)=(1)/(2)V_(1)`
`P_(2)=P_(1)((V_(1))/(V_(2)))^(gamma)` [for diatomic gas `gamma=1.4`]
`P_(2)=P_(1)((V_(1)xx2)/(V_(1)))^(1.4)" "P_(2)=P_(1)(2)^(1.4)=(1)^(1.4)P`