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Atmospheric Thermodynamics

Atmospheric Thermodynamics

As you climb a mountain, lower pressure lets air expand and cool on its own; that is adiabatic cooling. The dry adiabatic lapse rate is about 10°C/km, and when vapor condenses latent heat is released so cooling slows to the moist rate of about 5°C/km. The altitude where a parcel reaches the dew point becomes the cloud base, and air descending over a mountain compresses and warms as the Foehn effect. Here you can change surface temperature and environmental lapse rate to explore cloud-base height and atmospheric stability.

Why does it get cold as you climb a mountain?
💡 Intuition for adiabatic change
①Air at the surface rises up the mountain
②Higher altitude → lower air pressure (less compression)
③Lower pressure → expansion → temperature drops
④This is 'adiabatic cooling' — cooling without heat exchange
⑤Conversely, descending air compresses → adiabatic heating (Foehn effect!)
How are clouds formed?
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☁️ Cloud formation process
①Air parcel rises → pressure ↓ → expansion → temperature ↓
②Dry adiabatic lapse rate: ~10°C/km
③At some altitude, temperature reaches the dew point → condensation begins
④Altitude where condensation begins = cloud base (lifting condensation level)
⑤Beyond that, latent heat is released, slowing cooling → moist adiabatic lapse rate (~5°C/km)
Atmospheric stability — 3 cases
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Stability criterion
Unstable: Γenv > Γdry (10°C/km)
Rising air warmer than surroundings → continues rising → strong convection
Stable condition
Stable: Γenv < Γmoist (5°C/km)
Rising air cooler than surroundings → sinks back → convection suppressed
📐 Why does stability matter?
①Unstable atmosphere → cumulus (puffy) clouds → showers, thunderstorms
②Stable atmosphere → stratus clouds (fog, drizzle)
③Conditional instability: stable when dry, unstable when water vapor condenses
④Key to weather forecasting: analyze atmospheric stability to predict weather
Foehn effect in real life
🏔️ Hot winds across mountains
①Moist air rises a mountain → cools at moist adiabatic lapse rate (5°C/km)
②Rains near the summit (releases moisture)
③Descends past the peak → drier air → warms at dry adiabatic lapse rate (10°C/km)
④Result: hot dry wind on the leeward side (Foehn effect)
⑤Start 25°C, 2 km mountain: cooling -10° → 15°C, warming +20° → 35°C!
Worked Examples and Exam Practice
Example 1
When a dry air parcel rises 2 km, applying the dry adiabatic lapse rate (about 10°C/km), how much does its temperature drop?
1
The dry adiabatic lapse rate is about 10°C/km. Temperature change = lapse rate × height risen.
2
10°C/km × 2 km = a 20°C drop.
▸ About a 20°C drop
Without condensation it cools at 10°C/km (dry); once condensation starts it cools more slowly at about 5°C/km (moist).
Example 2
The surrounding air has an environmental lapse rate of 12°C/km. With a dry adiabatic lapse rate of 10°C/km, is this air stable or unstable for dry air?
1
If the environmental lapse rate exceeds the dry adiabatic rate, a rising parcel stays warmer than its surroundings and keeps rising.
2
Since 12°C/km > 10°C/km, it is (absolutely) unstable → active convection and cumulus clouds.
▸ Unstable (environmental 12°C/km > dry 10°C/km)
An environmental rate greater than the adiabatic rate means unstable; smaller means stable. Instability brings showers and thunderstorms.
CSAT-style
Which statement about adiabatic change and atmospheric stability is correct?
①The dry adiabatic lapse rate is smaller than the moist one
②Rising air expands adiabatically and its temperature falls
③If the environmental lapse rate is smaller than the adiabatic rate, the air is unstable
④Latent heat is absorbed when water vapor condenses
⑤Cumulus clouds develop well in stable air
▸ ② Rising air expands adiabatically and its temperature falls
1
Rising air meets lower pressure, expands, and cools on its own without heat exchange (adiabatic cooling).
2
The dry rate (10) exceeds the moist (5) (①), a smaller environmental rate means stable (③), condensation releases latent heat (④), and cumulus clouds develop in unstable air (⑤).
Summary
Key numbers
Dry adiabatic ≈ 10°C/km | Moist ≈ 5°C/km
cooling rate differs depending on whether water vapor condenses
🎯 Exam Points
①Dry adiabatic ≈ 10°C/km, moist adiabatic ≈ 5°C/km
②Γ_env > Γ_dry → absolute instability (strong convection)
③Γ_env < Γ_moist → absolute stability (convection suppressed)
④Γ_moist < Γ_env < Γ_dry → conditional instability
⑤Unstable → cumulus (showers), stable → stratus (drizzle)
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