A container of volume `4V_(0)` made of a perfectly non`-` conducting material is divided into two equal parts by a fixed rigid wall whose lower half is non`-` conducting and upper half is purely conducting. The right side of the wall is divided into equal parts `(` initially `0` by means of a massless non`-` conducting piston free to move as shown . Section`A` constains `2 mol` of a gas while the section `B` and `C` contain ` 1 mol` each of the same gas `( gamma = 15. )` at pressure `P_(0)` . The heater in left part is switched on till the final pressure in section `C` becomes `125//27 P_(0)`. Calculate

Final temperature in part `C`.

Options

A. `(P_0 V_0)/R`
B. `5/3 (P_0 V_0)/R`
C. `(P_0 V_0)/(3R)`
D. `(5 P_0 V_0)/R`

Answer

B

Explanation

`(P_0 V_0)/T_0 = ((125/27 P_0)((41V_0)/25))/(T_B) rArr T_B = 205/27 T_0 rArr T_B = 205/27 (P_0V_0)/R`