$3.[22$ Points$]$ Air at $75$ kPa is in a spring loaded piston$-$cylinder device with an initial volume of $1\backslash (\backslash$mathrm$\{$m$\}^\{\backslash$wedge$\}3\backslash )$ and initial temperature of $\backslash (25^\{*\}\backslash$mathrm$\{$C$\}\backslash ).$ The air is heated until the volume is $2$ times the initial volume.

a$)[8$ Points$]$ Calculate the heat into the system and the work of the air. Report your answer for both in kJ $.$

b$)[3$ Points$]$ Draw a Pressure $\backslash ((\backslash$mathrm$\{$kPa$\})\backslash )$ vs Specific Volume $\backslash (\backslash$left$(\backslash$mathrm$\{$m$\}^\{\backslash$wedge$\}3/\backslash$mathrm$\{$kg$\}\backslash$right$)\backslash )$ graph and plot the state transition.

c$)[8$ Points$]$ If the diameter of the piston and cylinder is $1$ meter, what is the force applied by the air on the piston in kN $?$ What is the final displacement of the piston in meters?

d$)[3$ Points$]$ Draw a Force $\backslash ((\backslash$mathrm$\{$kN$\})\backslash )$ vs displacement $\backslash ((\backslash$mathrm$\{$m$\})\backslash )$ graph for the state transition.