Suppose ideal gas equation follows `VP^(3) = contant`. Initial temperature and volume of the gas are T and V respectively. If gas expand to `27V` temperature will become

Options

A. T
B. 9T
C. 27T
D. T/9

Answer

B

Explanation

(b) `VP^(3)="constant" =k implies P=(k)/(V^(1//3))`
Also `PV=muRTimplies (k)/(V^(1//3)).V=muRTimpliesV^(2//3)=(muRT)/(k)`
Hence `((V_(1))/(V_(2)))^(2//3)=(T_(1))/(T_(2))implies ((V)/(27V))^(2//3)=(T)/(T_(2))impliesT_(2)=9T`