`1mm^3` of a gas is compressed at 1 atmospheric pressure and temperature `27^@C` to `627^@C`. What is the final pressure under adiabatic condition `(gamma` for the gas `=1.5`)

Options

A. `27xx10^5 N//m^2`
B. `80xx10^5 N//m^2`
C. `36xx10^5 N//m^2`
D. `56xx10^5 N//m^2`

Answer

A

Explanation

For adiabatic process `T^(gamma)P^(-(gamma-1))` = constant
`implies ((P_2)/(P_1))^(1//2)=((T_2)/(T_1))^(3//2)` [as `gamma` = 3/2]
`implies ((P_2)/(10^5))^(1//2)=((627+273)/(27+273))^(3//2)`
`P_2=27xx10^5 N//m^2`.