A piston$-$cylinder device contains $0\mathrm{.}05$ m of a gas initially at $200$ kPa. At this state, a linear spring that has a spring constant of $150$ kN$/$m is touching the piston but exerting no force on it$.$ Now heat is transferred to the gas, causing the piston to rise and to compress the spring until the volume inside the cylinder doubles. If the cross$-$sectional area of the piston is $0\mathrm{.}25$ m$,$ determine $($a$)$ the final pressure inside the cylinder, $($b$)$ the total work done by the gas, and $($c$)$ the fraction of this work done against the spring to compress it$.$