10 litre of a non linear polyatomic ideal gas at `127^(@)C` and 2 atm pressure is suddenly released to 1 atm pressure and the gas expanded adiabatically against constant external pressure. The final temperature and volume of the gas respectively are.

Options

A. T=350K,V = 17.5L
B. T = 300 K ,V = 15 L
C. T = 250 K, V = 12.5 L
D. None of these

Answer

A

Explanation

`DeltaU=w`
`nxx(R )/(gamma-1)(T_(2)-T_(1))=-P_("ext")((nRT_(2))/(P_(2))-(nRT_(1))/(P_(1)))`
`3(T_(2)-T_(1))=-1((T_(2))/(1)-(T_(1))/(2)]`
`3T_(2)-3T_(1)=-T_(2)+(T_(1))/(2)`
`4T_(2)=(7T_(1))/(2)`
`T_(2)=(7T_(1))/(8)=(7xx400)/(8)=350 K`
`(P_(1)V_(1))/(T_(1))=(P_(2)V_(2))/(T_(2))implies(2xx10)/(400)=(1xxV_(2))/(350)impliesV_(2)=17.5 L`