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

Making a state table.

Making a process table.

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

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

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 $3\mathrm{.}0$ moles of nitrogen gas $($diatomic$).$ During the process $ab,$ the pressure rises by a factor of $3\mathrm{.}0.$

Engine Cycle

Solution

$(1)$ Fill in the State Table $($all pressures in Pascals, all volumes in cubic meters, all temperatures in K$).$

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

$(3)$ Find the Totals:

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

$\backslash$table$[[$Pressure Volume Temperature,$],[$a$,],[$b$,],[$c$,]]$

Work $=$ J

Heat $=,$ J

$dU=$

$Q-$hot $=,J$

$Q-$cold $=,J$

efficiency $=\%$