The diesel cycle includes two adiabatic processes, a high temperature isobaric process, and a low temperature isochoric process. $($This is an all symbolic problem. Use subscripts to distinguish different volumes and pressures. Assume all heat capacities and ratios of heat capacities are known. Do not use temperature. If there is no function possible, say why.$)$

a$.$ Draw a PV diagram for the cycle. Start your cycle at the lowest pressure and highest volume and label the corners $a,b,c,d.$

b$.$ What your equation of $P(V)$ from a to b $?$ Use that equation to determine the work done from a to $b.($do the integral$)$

c$.$ What your equation of $P(V)$ from b to c $?$ Use that equation to determine the work done from $b$ to c $.($do the integral$)$

d$.$ What your equation of $P(V)$ from c to d $?$ Use that equation to determine the work done from c to d$.($do the integral$)$

e$.$ What your equation of $P(V)$ from d to a $?$ Use that equation to determine the work done from d to a$.($do the integral$)$

f$.$ What is the total work done during this process?