An ideal gas at pressure of 1 atmosphere and temperature of `27^(@)C` is compressed adiabatically until its pressure becomes 8 times the initial pressure, then the final temperature is `(gamma=3//2)`

Options

A. `627^@ C`
B. `527^@ C`
C. `427^@ C`
D. `327^@ C`

Answer

D

Explanation

For adiabatic process -
`(T)/(P^(((gamma-1)/(gamma))))` = constant
Then `(T_2)/(T_1)=((P_2)/(P_1))^((gamma-1)/(gamma))= (8)^((3/2-1)/(3//2))` = 2
`implies T_2=2T_1 implies T_2 = 2(273+27)`
= 600 K = `327^@C`.