A gas undergoes an adiabatic process in which pressure becomes `((8)/(3 sqrt(3)))` times and volume becomes `(3)/(4)` of initial volume. If initial absolute temperature was `T` , the final temperature is

Options

A. `(32T)/(9sqrt(3))`
B. `(2T)/(sqrt(3))`
C. `T^(3/2)`
D. `(sqrt(3)T)/(2)`

Answer

B

Explanation

For adiabatic process `P_(1)V_(1)^(gamma) = P_(2)V_(2)^(gamma) implies P_(0)V_(0)^(gamma) = ((8)/(3sqrt(3))P_(0)) ((3)/(4)V_(0))^(gamma)` `(" …")` (i)
Also , `T_(1)V_(1)^(gamma-1) = T_(2)V_(2)^(gamma-1) = implies TV_(0)^(gamma-1) = T_(2)((3)/(4)V_(0))^(gamma-1)` `( .....)` (ii) Solving (i) &(ii) , `T_(2) = (2T)/(sqrt(3))`