$1.)$ An expandable cylinder that has a piston with a cross$-$sectional area of $0\mathrm{.}0100$m$2$ and negligible mass has its top connected to a spring with a spring constant of $2000$N$/$m$.$ The cylinder is filled with $5\mathrm{.}00$L of gas when the spring was relaxed at a pressure of $1\mathrm{.}013$x$105$Pa $(1\mathrm{.}00$ atm$)$ and a temperature of $20\mathrm{.}0$C$.$ If the temperature is increased to $250$C : a$.$ How high does the cylinder rise?

b$.$ What is the Pressure of the gas?