A container with insulating walls is divided into two equal parts by a partition fitted with a valve. One part is filled with an ideal gas at a pressure P and temperature T, whereas the other part is completely evacuated . If the valve is suddenly opened, the pressure and temperature of the gas will be

Options

A. `(P)/(2), T`
B. `(P)/(2), (T)/(2)`
C. `P , T`
D. `P , (T)/(2)`

Answer

A

Explanation

This is free expansion of the gas in which temperature will remain constant i.e. on the other side temperature will `T`.
Number of moles `n_(1) = (PV//2)/(KT)`
Finally number of moles `n_(2) = (P'V)/(KT)`
`n_(1) = n_(2)`
`(PV)/(2) = (P^(1)V)/(KT) implies P' = (P)/(2)`