The fixed non-conducting cylinder shown in figure has a noconducting heavy piston of mass `M` that can slide without friction. The area of piston is `S` and the cylinder is filled with an ideal gas `(lambda=1.5)` with an initial volume `V` and an initial pressure `P`. Assume that the outside pressure on the piston is zero (vaccum). (Neglect acceleration due to gravity).

For the temperature of the gas to drop to one half of its original value. the piston will have to move by a distance:

Options

A. `(V)/(S)`
B. `(2V)/(S)`
C. `(3V)/(S)`
D. `(5V)/(S)`

Explanation

`(T_(f))/(T)=((V)/(V_(1)))^(lambda-1)=sqrt((V)/(V+LS))=(1)/(2)`
`thereforeL=(3V)/(S)`