A mass of diatomic gas (`gamma` = 1.4) at a pressure of 2 atmosphere is compressed adiabatically 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

PV'=constant
`T_(1)=273+27 =300 K`
`P(T/P)^(gamma)`=constant
`T_(2)=273+927=1200 K`
`P^(1-gamma)T^(gamma)`=constant
`rArr P^(f-gamma)T_(1)^(gamma)=P_(2)^(1-gamma)T_(2)^(gamma)`
`rArr 2_(1)^(1-1.4) (300)^(1.4) =P_(2)^(1-1.4) .(1200)^(1.4)`
`rArr ((P_(2))/(P_(1)))^(1-gamma)=((T_(1))/(T_(2)))^(gamma)`
`rArr ((P_(2))/(P_(1)))=((T_(1))/(T_(2)))^((gamma)/(1-gamma))`
`((P_(1))/(P_(2)))^(1-gamma)=((T_(2))/(T_(1)))^(gamma)rArr ((P_(1))/(P_(2)))^(1-1.4)=(1200/300)^(1.4)rArr ((P_(1))/(P_(2)))^(-0.4)=(4)^(1.4)`
`((P_(2))/(P_(1)))^(0.4)=4^(1.4)rArr P_(2)=P_(1)4^((1.4/0.4))=P_(1)4^((7/2))`
`=P_(1)(2^(7))=2xx128=256`