The Physics of Hot Air Balloons
A hot air balloon is Archimedes' principle you can ride in. Heating the air inside the envelope makes it less dense than the cool air outside — and the displaced cool air's weight lifts the whole craft.
Buoyancy from density difference
Lift equals the weight of displaced cool air minus the weight of the hot air inside. Heat air from 15 °C to 100 °C and its density drops ~25% — over a 2,200 m³ envelope that's tonnes of lift.
Ideal gas law at work
At roughly constant pressure, PV = nRT means heating the gas expands it: some air escapes the envelope's open bottom, so fewer molecules remain inside — lower density, same volume.
Altitude control
The burner is the throttle: fire it to climb, let the air cool to descend. Pilots steer by finding winds at different altitudes — there is no rudder.
Why mornings?
Balloons fly at dawn because the air is cool (denser outside air = more lift) and calm — thermals and wind later in the day make flight rough and landings hard.
Try this yourself
- Hold a tissue-paper 'balloon' over a toaster (carefully!) and watch hot air lift it.
- Compute air density at 15 °C vs 100 °C with ρ = P/RT and find the percentage lift gain.