A volume V of a gas at a temperature `T_1` and a pressure P' is enclosed in a sphere. It is connected to another sphere of volume `(V)/(2)` by a tube and stop cock. The second sphere is initially evacuated and the stop cock is closed. If the stop cock is opened the temperature of the gas in the second sphere becomes `T_(2)`. The first sphere is maintained at `'T_1'`, what is the final pressure within the apparatus.

Options

A. `(2PT_(2))/(2 T_(2) + T_(1))`
B. `(2 PT_(2))/(T_(2) + 2 T_(1))`
C. `(2 PT_(2))/(2 T_(2) + T_(1))`
D. `(2PT_(2))/(T_(1) + T_(2))`

Answer

A

Explanation

Moles of gas in 1st sphere = `(PV)/(RT_(1))`
After stop clock is opened , Moles in first sphere = `(P_(1) V)/(RT_(1)) `, Moles in second spheres = `((P_(1)V)/(2))/(RT_(1))`
`(PV)/(RT_(1)) = (P_(1) V)/(RT_(1)) + (P_(1)V)/(3RT_(2)) , P_(1) = (2PT_(2))/(2 T_(2) + T_(1))`