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 `A`.

Options

A. `(12P_(0)V_(0))/(13R)`
B. `(P_(0)V_(0))/(R)`
C. `(105P_(0)V_(0))/(13R)`
D. `(205P_(0)V_(0))/(27R)`

Answer

D

Explanation

For `'C',P_(0)V_(0)^(gamma)=(125/27)P_(0)V_(C)^(gamma)`
`V_(C)=V_(0)(9/25) , V_(B)=2V_(0)(9V_(0))/25=((50-9))/25V_(0)`
`V_(B)=41/25V_(0) , T_(0A)=T_(0B)=(P_(0)V_(0))/R`
`T_(C)=(125/27P_(0)xx9/25V_(0))/R=(5P_(0)V_(0))/(3R)`
`T_(B)=(125/27P_(0)xx41/25V_(0))/R=205/27(P_(0)V_(0))/(R)=T_(A)`
`Q=DeltaU`
`Q=n_(A)C_(v)(T_(A)-T_(0))+n_(b)C_(v)DeltaT_(B)+n_(c)C_(v)DeltaT_(c)=368/9P_(0)V_(0)`