A gas fills the right portion of a horizontal cylinder whose radius is `5.00 cm`. The initial pressure of the gas is `101 kPa`. A frictionless movable piston separates the gas from the left portion of the cylinder, which is evacuated and contains an ideal spring, as the drawing shows. The piston is initially unstrained, and the length of the gas-filled portion is `20.0 cm`. Wheen the pin is removed and the gas is allowed to expand, the length of the gas-filled chamber doubles when it finally reaches equilibrium. The initial and final temperatures are equal. Determine the spring constant of the spring.

Options

A. `200 N//m`
B. `20 N//m`
C. `2 N//cm`
D. `2 N//mm`

Answer

D

Explanation

The final pressure is `p = (101)/(2)kPa , kx = p pi r^(2)` where `x = 0.2`, the compression in the spring and `r = 0.05` the radius of cylinder.