$2\mathrm{.}18$ Carbon dioxide $(C{O}_2)$ gas within a piston$-$cylinder assembly undergoes a process from a state where $p_1=5lb\frac{f}{i}{n}^2.{?}^2,V_1=2\mathrm{.}5f{t}^3$ to a state where $p_2=20lb\frac{f}{i}n.{?}^2,V_2=0\mathrm{.}5f{t}^3.$ The relationship between pressure and volume during the process is given by $p=23\mathrm{.}75-7\mathrm{.}5V,$ where $V$ is in $f{t}^3$ and $p$ is in lbf$/$in$.{?}^2$ Determine the work for the process, in Btu.