An ideal gas is kept in two adjacent chambers of volume V and 2V, separated by a thin partition, under initial conditions as shown in figure. The chamber is adiabatic i.e., no heat flows in or out. Now the partition is removed and the gas is allowed to stabilize. If `P_f` and `T_f` are the values of final pressure and temperature, then :

Options

A. `P_f = 5/3 P`
B. `P_f = p `
C. `P_f/T_f = 8/9 P/T`
D. `T_f = 3/2 T`

Answer

C, D

Explanation

`P_1 V_1 + P_2 V_2 = P_f V_f rArr 2 PV + 2PV = P_f (3V) rArr P_f=(4P)/3`
`n_1 = (2 PV)/(RT) & n_2 = (2 PV)/(R(3T)) rArr n_1 + n_2 = (8 PV)/(3RT)`
`P_fV_f =(n_1 +n_2) "R T"_f rArr(4P)/3 (3V) =(8 PV)/(3RT) .(RT_f) rArr T_f =(3T)/2 " "rArr" "P_f/T_f = (8P)/(9T)`