One mole of a monoatomic ideal gas occupies two champers of a cylinder partioned by means of a movable pision. The walls of the cylinder as well as the piston are thermal insulators. Initially equal amounts of gas fill both the chambers at (`P_(0), V_(0), T_(0)`). A coil is burnt in the left chamber which absorbs heat and expands , pushing the piston to the right . The gas on the right chamber is compressed until to pressure becomes `32 P_(0)`.

` The final volume of left chamber is

Options

A. `(V_(0_))/(8)`
B. `(15)/(8)V_(0)`
C. `(7)/(8)V_(0)`
D. `(9)/(8)V_(0)`

Answer

B

Explanation

Since the compression on the right is adiabatic so `P_(0)V_(0)^(gamma) = P_(R)V_(R)^(gamma)`
`implies P_(0)V_(0)^(5//3) = 32P_(0)V_(R)^(5//3) implies V_(R) = (V_(0))/(8) implies V_(L) = V_(0) + (7)/(8)V_(0) = (15)/(8)V_(0)`