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

Options

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

Answer

D

Explanation

In an adiabatic process `T^(gamma)P^(1-gamma)` = Constant
`T_(1)^(gamma)P_(1)^(1-gamma)=T_(2)^(gamma)P_(2)^(1-gamma)`
`implies (T_(1)/T_(2))^gamma=(P_(2)/P_(1))^(1-gamma)`
`implies ((300)/T_(2))^(3//2)=((8P_(1))/P_(1))^(1-(3//2)`
`implies T_(2)^(3//2)= (300)^((3//2))xx8^(1//2)`
`implies T_(2)^(3)=300^(3) xx 8`
`therefore T_(2)=600 K= 327^(@)C`