If the Carnot cycle is represented on a graph of pressure of the
gas against its volume (a pV diagram) we
get a clear view of how much work is done in a complete cycle. 

Remember that the work done when a gas changes volume,
at constant pressure, is given
by 



The product of pressure and volume is represented by an area
on a
pV diagram. 

The area under the curve on a pV diagram tells us the work done
during the process. 

This can be found by adding up the areas of lots of thin
rectangles, each of which corresponds to a constant (or very
nearly constant) pressure. 

(Mathematically we say we are
integrating the equation of the curve to find the area below
it.) 


The numbers in brackets refer to the diagrams representing the Carnot cycle 


Curve A (2 to 3) 
Isothermal expansion at T_{H} (the temperature of the
source) 

Work done by the gas 
















Curve B (4 to 5) 
Adiabatic expansion 

Work done by the gas 













The area under these two curves represents the
total work done by the gas during one cycle 







Curve C (6 to 7) 
Isothermal compression at T_{C} (the temperature of the
sink) 

Work done on the gas 
















Curve D (8 to 1) 
Adiabatic compression 

Work done on the gas 













The area under these two curves represents the
total work done on the gas during one cycle 




The area enclosed by the four curves is equal to the
difference between the two pervious areas and so represents
the net work done by the engine per cycle 



This shows why the the efficiency of a heat engine depends on
the difference between the temperatures of source and sink. 

The area enclosed by the cycle will be greater if curve A moves
up and/or curve C moves down on the pV diagram. 
