The Open Door Web Site
THERMAL PHYSICS
 Custom Search
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.
 © The Open Door Team2019Any questions orproblems regardingthis site should beaddressed tothe webmaster © David Hoult 2019 Hosted By

Thermal Physics Index Page
 Message to all Open Door Web Site users 2019 marks the 20th anniversary of the Open Door Web Site and, sadly, its last year. We have tried very hard to keep the ODWS online but it has become too costly. We tried Google Ads to cover costs but stopped when it became apparent that we could not prevent inappropriate advertisements from appearing. Thanks to those of you who have supported the ODWS in the past. Your contributions have been much appreciated. Wishing you all a peaceful, happy and successful 2019 Shirley BurchillWebmaster