p–V Diagrams (AQA A Level Physics): Revision Note

p–V diagrams

• When a gas expands, it does work on its surroundings by exerting pressure on the walls of the container it's in

• For a gas inside a piston, the force exerted by the gas pushes the piston outwards

  • As a result, work is done by the gas when the piston expands the volume of the gas

• Alternatively, if an external force is applied to the piston, the gas will be compressed

  • In this case, work is done on the gas when the piston compresses the gas

• The work done when the volume of a gas changes at constant pressure is:

$W=p∆V$

• Where:

  • $W$ = work done (J)

  • $p$ = pressure of the gas (Pa)

  • $∆V$ = change in the volume of the gas (m³)

• This equation assumes that the surrounding pressure does not change as the gas expands

  • This is true if the gas is expanding against the pressure of the atmosphere, which changes very slowly

p-V diagrams

• Pressure-volume (p-V) diagrams are often used to represent changes in the state of a gas in thermodynamic processes

• The area under a p-V diagram is equal to the work done

• When a gas expands (at constant pressure), work done is positive

  • Volume increases $+∆V$

  • Work is done by the gas $+W$

• When a gas is compressed (at constant pressure), work done is negative

  • Volume decreases $-∆V$

  • Work is done on the gas $-W$

• When both the volume and pressure of gas changes, the work done can be determined from the area under a p-V diagram

• In the context of engines, these are referred to as indicator diagrams