11.2.2 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

Gas pushed in a piston

The expansion of the gas does work on the piston by exerting a force over a distance, s

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

• Where:
  • W = work done (J)
  • p = pressure of the gas (Pa)
  • ΔV = 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

Gas expanding and compressing in a cylinder by a piston

Positive or negative work done depends on whether the gas is compressed or expanded

• The area under a p–V diagram tells us how much work is done
• When a gas expands (at constant pressure) work done is positive
  • Volume increases +ΔV
  • Work is done by the gas +W

• When a gas is compressed (at constant pressure) work done W is negative
  • Volume decreases −ΔV
  • 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