A closed and isolated cylinder contains ideal gas. An adiabatic separator of mass m, cross sectional area `A` divides the cylinder into two equal parts each with volume `V_(0)` and pressure `P_(0)` in equilibrium Assume the sepatator to move without friction.
If the piston is slightly displaced by x, the net force acting on the piston is

Options

A. `(P_(0)gammaA^(2)x)/(V_(0))`
B. `(2P_(0)gammaA^(2)x)/(V_(0))`
C. `(3P_(0)gammaA^(2)x)/(V_(0))`
D. `(P_(0)gammaA^(2)x)/((gamma-1)V_(0))`

Answer

B

Explanation

`DeltaQ=0` for system `P_(0)V_(0)^(gamma)=P_(1)V_(1)^(gamma)=P_(2)V_(2)^(gamma)`
`impliesP_(1)=P_(0)[1-(gammaAx)/(V_(0))]impliesP_(2)=P_(0)[1+(gammaAx)/(V_(0))]`
` implies F = (2P_(0)gammaA^(2)x)/(V_(0)`