pV Diagrams and Work Done

It is often useful to represent the changes that happen to a gas during a thermodynamic process on adiagram. This is a graph of pressure,against volume,The volume is usually put on the- axis and the pressure on the- axis. These graphs are useful because the area under the graph represents the work done on the gas or by the gas.

More generally, there are exchanges of heat between the gas and its' surroundings. If the gas undergoes a 'cycle' as shown below, work is done on the gas as it contracts from 1 to 2. Between states 2 and 3, an amount of heatis absorbed. The pressure increases at constant volume. Between states 3 and 4, the gas expands and does work on its' surroundings, Finally, the gas gives up an amount of heatto its' surroundings, returning to it's original state 1.

The gas does a net amount of work A on its' surroundings, equal to the area under the graph between states 3 and 4 minus the area under the graph between states 1 and 2. This area is the difference betweenand