The Carnot cycle is a thermodynamic cycle whose pressure$-$volume

diagram gives a region $R_{VP},$ with positive $P$ and $V,$ in the $(V,P)$

plane bounded by the curves

$PV=nR{T}_1$

$PV=nR{T}_2$

$P{V}^{}=C_1$

$P{V}^{}=C_2,$

where $n,R,,T_1,T_2,C_1,C_2$ are positive constants satisfying $>1,$

$R_{VP}{R}_{st}(s,t)R_{VP}{C}_1.$

Introduce a map which maps the region $R_{VP}$ into a rectangle $R_{st}in$

the $(s,t)$ plane.

Then compute the area $of{R}_{VP}.T_1$ and $C_1.$

Introduce a map which maps the region $R_{VP}$ into a rectangle $R_{st}in$

the $(s,t)$ plane.

Then compute the area $of{R}_{VP}.$