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

The heat supplied by the heater.

Options

A. `(205 P_0 V_0)/(27 R)`
B. `(P_0 V_0)/R`
C. `(105 P_0 V_0)/(13R)`
D. None of these

Answer

A

Explanation

Process in C adiabatic
`P_0 V_0^(3//2) = ((125)/27 P_0)" "rArr " "V_C=((27)/(125))^(2//3) V_0 rArr V_C = 9/25 V_0`
`T_0 V_0^(1//2) = T_(C) (9/25 V_0)^(1//2)" "rArr" "T_C =5/3 T_0 rArr T_C =(5 P_0 V_0)/(3R)`