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

`T_(1) = 273+27=300K`
`T_(2) = 273+927=1200K`
Gas equation for adiabatic process `pV^(gamma)` = constant
`p((T)/(p))^(gamma)` = constant `( :' pV=RT)`
`(p_2)/(p_1)=((T_2)/(T_1))^((gamma)/(gamma-1)) or p_(2) = p_(1)((T_2)/(T_1))^((gamma)/(gamma-1))`
`p_(2) = 2((1200)/(300)^((1.4)/(1.4-1))`
`P_(2) = 256 atm`.