Adiabatic processes: why rising air cools
Imagine a large bubble of air called a parcel. It does not mix much with the air around it.
- Air pressure falls with height. A rising parcel has less air pushing on it, so it expands.
- To expand, it pushes the surrounding air away. That work uses its own energy, so its temperature falls.
- No heat goes in or out. A change like this is called adiabatic ("no heat crossing").
Sinking air is squeezed (compressed) and warms the same way. This is why air coming down a mountain feels warm and dry.
Lapse rate
A lapse rate is how fast temperature falls as you go up, in °C per km.
Dry, moist and environmental lapse rates
| Lapse rate | Value | What it describes |
|---|---|---|
| Dry adiabatic (DALR) | 10 °C/km (9.8) | rising unsaturated parcel |
| Saturated / moist adiabatic (SALR) | about 4 to 7 °C/km (we use 6) | rising cloudy parcel |
| Environmental (ELR) | average 6.5 °C/km, changes daily | the still air around the parcel |
Why the moist rate is smaller
When the parcel cools to its dew point, water vapour condenses into droplets. Condensation releases latent heat (the heat that was used to evaporate the water). This heat partly cancels the cooling, so a cloudy parcel cools more slowly. In very warm, humid air the rate is near 4 °C/km; in cold air it is near 7 to 9.
Cloud base
The height where the parcel reaches its dew point is the condensation level, the flat base of cumulus clouds. A quick rule: cloud base (m) ≈ 125 × (air temperature - dew point).
Stability: stable, unstable and conditionally unstable air
Stability tells us what a lifted parcel does next. Compare it with the air at the same height:
- Parcel colder than surroundings → denser → sinks back. Stable.
- Parcel warmer → lighter → keeps rising. Unstable.
| Condition | Name | Weather |
|---|---|---|
| ELR less than SALR (below about 6 °C/km) | absolutely stable | clear sky or flat layer clouds (stratus), drizzle, fog |
| ELR between SALR and DALR (6 to 10) | conditionally unstable | stable while dry; unstable once saturated, so humid air can grow big cumulus |
| ELR greater than DALR (above 10) | absolutely unstable | strong rising currents, often only near hot ground |
| Temperature rises with height | inversion (very stable) | fog, haze, smog trapped near the ground |
How stability shapes clouds
Stable air spreads clouds sideways into flat sheets (stratus, stratocumulus). Unstable air builds clouds upward: cumulus, then towering cumulonimbus with heavy rain, hail and lightning. Air is lifted by surface heating (convection), mountains (orographic lift), fronts and converging winds.
Applications: storms, warm mountain winds and smog
- Afternoon thunderstorms form when hot ground and humid air make the lower atmosphere unstable.
- Foehn / chinook winds: moist air rises up one side of a mountain (cooling at the moist rate, raining) and sinks down the other side dry (warming at the dry rate), so it arrives warmer and drier.
- Inversions on clear, calm nights trap pollution in valleys and cities.
- Pilots and weather services measure the ELR with weather balloons (radiosondes) twice a day to forecast storms.
Try it: predict the parcel
- Open the last 3D step. Set the surrounding lapse rate to 4 °C/km. Predict: high or low? Check.
- Set it to 9 °C/km with dew point 22 °C. Predict, then watch the cloud grow.
- Keep 9 °C/km but lower the dew point to 8 °C. Why does the parcel now stop? (Hint: it never gets cloudy, so it keeps cooling at 10 °C/km.)
- At home: pump a bicycle tyre and feel the pump get warm (compression warms air). Let air out of the tyre valve and feel it cool (expansion cools air).
Key formulas and definitions
- Parcel below cloud base: T = T₀ - 10 × h (h in km)
- Parcel above cloud base: T = T_base - 6 × (h - h_base)
- Environment: T = T₀ - ELR × h
- Cloud base height (m) ≈ 125 × (T - dew point)
- Stable if parcel colder than surroundings; unstable if warmer
Worked examples
1. Dry air at 25 °C rises 2 km. What is its temperature?
It cools at the dry rate: 25 - 10 × 2 = 5 °C.
2. Ground air is 30 °C with dew point 22 °C. Find the cloud base height.
Gap = 30 - 22 = 8 °C. Cloud base ≈ 125 × 8 = 1000 m = 1 km.
3. Using the last example, what is the parcel's temperature at 3 km?
To 1 km (dry): 30 - 10 = 20 °C. Then 2 km more at about 6 °C/km: 20 - 12 = 8 °C.
4. At 3 km the surrounding air (ELR 9 °C/km, ground 30 °C) is how warm? Is the parcel from the last example stable or unstable there?
Environment: 30 - 9 × 3 = 3 °C. The parcel is 8 °C, which is 5 °C warmer, so it is lighter and keeps rising: unstable. Expect tall cumulonimbus.
5. Foehn: air at 20 °C at sea level rises over a 3 km mountain. Cloud base is at 1 km. It rains out and descends dry to sea level on the other side. Final temperature?
Up to 1 km dry: 20 - 10 = 10 °C. 1 km to 3 km moist: 10 - 6 × 2 = -2 °C. Down 3 km dry: -2 + 10 × 3 = 28 °C. It arrives 8 °C warmer and much drier.
6. A balloon measures 15 °C at the ground and 18 °C at 300 m. What is this and what weather is likely?
Temperature rises with height: an inversion, very stable air. Smoke and fog stay trapped near the ground; expect haze or smog and calm conditions.
Common mistakes
- Thinking rising air cools because it is 'closer to space' or meets cold air. It cools because it expands; no heat leaves it.
- Mixing up the environmental lapse rate (the still air around) with the adiabatic rates (the moving parcel).
- Saying moist air cools faster. It cools slower, because condensation releases latent heat.
- Deciding stability from the parcel alone. Stability is always a comparison: parcel vs surroundings at the same height.