Goal Solve for the efficiency of a heat engine using a five$-$step process the includes:

$1.$ Making a state table.

$2.$ Making a process table.

$3.$ Calculating the totals for Work, Heat, and Internal$-$Energy$-$Change.

$4.$ Identifying the heat input $($hot reservoir$)$ and output $($cold reservoir$).$

$5.$ Calculating the efficiency of the engine.

Problem Shown in the figure to the right is a cyclic process undergone by a heat engine. Your heat engine shall use $5\mathrm{.}0$ moles of nitrogen gas $($diatomic$).$ During the process a$->$b$,$ the pressure rises by a factor of $5\mathrm{.}0.$ T$\_$a$=300$K$,$ P$\_$a$=100,000$Pa$,(1)$ Fill in the State Table $($all pressures in Pascals, all volumes in cubic meters, all temperatures in K$).$

PressureVolumeTemperatureabc

$(2)$ Fill in the Process Table $($all entries in Joules$).$

WorkHeatdUa$->$bb$->$cc$->$a

$(3)$ Find the Totals:

Work $=$ JHeat $=$ JdU $=$ J

$(4)$ Find the heat input $($from "cold reservoir"$)$ and the heat output $($to "hot reservoir"$)$:

Q$-$hot $=$ JQ$-$cold $=$ J

$(5)$ Find the performance coefficient of the refrigerator:

Coefficient $=$