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p-V Diagram for the Carnot Cycle
If the Carnot cycle is represented on a graph of pressure of the gas against its volume (a p-V 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 p-V diagram.  
The area under the curve on a p-V 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 TH (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 TC (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 p-V diagram.  
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