• When a gas expands, it does work on its surroundings by exerting pressure on the walls of the container it's in
• This is important, for example, in a steam engine where expanding steam pushes a piston to turn the engine
• The work done when a volume of gas changes at constant pressure is defined as:

W = pΔV

• Where:
  • W = work done (J)
  • p = external pressure (Pa)
  • V = volume of gas (m3)

   

• For a gas inside a cylinder enclosed by a moveable piston, the force exerted by the gas pushes the piston outwards
• Therefore, the gas?does work on the piston

The gas expansion pushes the piston a distance s

Derivation

• The volume of gas is at constant pressure. This means the force?F?exerted by the gas on the piston is equal to :

F = p × A

• Where:
  • p?= pressure of the gas (Pa)
  • A?= cross-sectional area of the cylinder (m2)

   

• The definition of work done is:

W = F × s

• Where:
  • F?= force (N)
  • s?= displacement in the direction of force (m)

   

• The displacement of the gas?d?multiplied by the cross-sectional area?A?is the increase in volume ΔV of the gas:

W = p × A × s

• This gives the equation for the work done when the volume of a gas changes at constant pressure:

W = pΔV

• Where:
  • ΔV?= increase in the volume of the gas in the piston when expanding (m3)

   

• This is assuming that the surrounding pressure?p?does not change as the gas expands
• This will be true if the gas is expanding against the pressure of the atmosphere, which changes very slowly
• When the gas?expands?(V?increases), work is done?by?the gas
• When the gas is?compressed?(V?decreases), work is done?on?the gas

Step 1:?Write down the equation for the work done by a gas

W = pΔV

Step 2:?Substitute in values

ΔV = final volume ? initial volume = 0.030 ? 0.015 = 0.015 m3

W = (1.0 × 105) × 0.015 = 1500 J