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

`P_1=1atm,T_1=27^@C=27+273=300K`
`P_2=8atm,T_2=?`
`(T_1^(gamma))/(P_1^(gamma-1))=(T_2^(gamma))/(P_2^(gamma-1))`
`((T_2)/(T_1))^(gamma)=((P_2)/(P_1))^(gamma-1)`
`(T_2)/(T_1)=((P_2)/(P_1))^((gamma-1)/(gamma))`
`(T_2)/(300)=((8)/(1))^(((3)/(2)-1)/((3)/(2)))=(8)^((1)/(3))=(2^3)^((1)/(3))=2`
`T_2=600K=600-273=327^@C`