$3.$ An air$-$filled piston$-$cylinder assembly starts at p$1=30$ Ibf$/$in$\text{'},$ Ti$=540\backslash$deg F$,$ andV, $=4$ ft$.$ The air undergoes a process to a final state of p$2=20$ Ibf$/$in$\text{'}$ and $2=4\mathrm{.}5$ ft$.$ During this process, $1$ Btu of work is done on the air by the paddle wheel, and $12$ Btu of heat is added to the air. Remember to pay attention to your units!$($a$)$ Calculate the temperature at state $2$ in $\backslash$deg R$.($b$)$ Determine the energy transfer by work from the air to the piston during this process.