The correct option is B 9T
Given,VP3=constant=k3 (say) ⇒P=kV1/3 ......(1)
Also for an ideal gas, PV=nRT
Using (1) in the above ideal gas equation, we get
kV1/3.V=nRT⇒V2/3=nRTk
∴ we can say that, V2/3∝T
Hence, (V1V2)2/3=T1T2 .....(2)
Given, Initial temperature (T1)=T
Initial volume (V1)=V
Final volume (V2)=27V
Final temperature (T2)=?
Equation (2) becomes
(V27V)2/3=TT2⇒T2=9T
Thus, option (b) is the correct answer.