$2\mathrm{.}55$ A piston$-$cylinder assembly $($see the sketch$)$ contains $0\mathrm{.}003m^3$ air at $25C.$

The gas forces on each side of the piston, assuming there are no frictional

forces at the piston$-$cylinder interface, balance the weight of the piston. The

piston has a cross$-$sectional area of $0\mathrm{.}02m^2$ and a mass of $150$ kg $.$ The atmos$-$

pheric pressure is $101\mathrm{.}35$ kPa $,$ and the local gravitational acceleration is

$9\mathrm{.}8\frac{m}{s^2}.$

A$.$ Determine the mass of air trapped within the cylinder.

B$.$ Determine the distance the piston moves in millimeters when a $450-N$

weight is placed on top of the piston. Assume the new equilibrium temperature

is still $25C.$

C$.$ In what way is the gas like a mechanical spring?