Work Done by a Gas
- 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
Worked example
When a balloon is inflated, its rubber walls push against the air around it.Calculate the work done when the balloon is blown up from 0.015 m3 to 0.030 m3.Atmospheric pressure = 1.0 × 105 Pa.
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
Exam Tip
The pressure p in the work done by a gas equation is not the pressure of the gas but the pressure of the surroundings. This is because when a gas expands, it does work on the surroundings.