A container of volume 4V(0) made of a pe...

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.

`(36B)/6 P_0 V_0`

`(113)/6 P_0 V_0`

`(315)/6 P_0 V_0`

`(368)/9 P_0 V_0`

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Verified by Experts

The correct Answer is:

`T_A = T_B = 205/27 (P_0 V_0)/R`
` C_V" for gas "= R/(gamma -1) = 2R`
As `Delta U = n C_V Delta T` for any process,
`Delta Q_(" heater") Delta U_A +Delta U_B + Delta U_C = 2 xx2 xxR (205/278 (P_0V_0)/R)+2R(205/27 (P_0 V_0)/R - (P_0 V_0)/R)`
` + 2R( 5/3 (P_0 V_0)/R - (P_0 V_0)/R ) = 368/9 P_0 V_0`

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