A mass of diatomic gas`(gamma=1.4)` at a pressure of 2 atomphere is compressed adiabitically so that its temperature rises from `27^(@)C` to `927^(@)C`. The pressure of the gas in the final state is

Options

A. `28 atm`
B. `68.7 atm`
C. `256 atm`
D. `8 atm`

Answer

C

Explanation

Here, `gamma=1.4, P_(1)= 2 atm , T_(1)= 273+27 = 300K`
`P_(2)=? , T_(2)= 927+273= 1200K`
As `P^(1-gamma)T^(gamma)=a constant`
`:. P_(2)^(1-gamma)T_(2)^(gamma)= P_(1)^(1-gamma)T_(1)^(gamma)`
or `(P_(2)/(P_(1)))^(1-gamma)=(T_(1)/T_(2))^(gamma)`
`(P_(2)/2)^(1-1.4)=((300)/(1200))^(1.4)=(1/4)^(1.4)` or `(P_(2)/2)^(-0.4)=(1/4)^(1.4)`
or `(2/(P_(2)))=(1/4)^(1.4)= 1/((4)^(1.4))`
or `P_(2)= 2xx(4)^(1.4..0.4)= 2xx(4)^(7//2)`
`=2xx128= 256 atm`