Almost every cloud forms in air that is rising. The reason is simple to state and surprising to explain: rising air cools. You know that pressure falls with height; this lesson shows why that makes a rising bubble of air colder, even though nothing outside cools it.
🔑 Key idea
A parcel (a bubble) of rising air moves into lower pressure, expands, and cools by about 9.8 °C for every kilometer it rises, as long as no water condenses in it. This is the dry adiabatic lapse rate ("adiabatic" means no heat flows in or out). Sinking air is squeezed and warms at the same rate.
💡 Why it works
As the parcel rises, the air around it presses less, so the parcel spreads out, pushing the surrounding air aside. Pushing is work, and the energy for it comes from the parcel's own molecules, which slow down: the parcel cools. Air is a poor conductor and the parcel moves fast, so almost no heat flows in to make up the loss. The rate comes from energy bookkeeping: for each kilogram, the drop in thermal energy $c_p\,\Delta T$ matches the gain in height energy $g\,\Delta z$, so $\Delta T/\Delta z = -g/c_p = -9.8 \div 1005 \approx -0.0098$ °C per meter, or 9.8 °C per km.
In the Science Lab's First Law lab, the first law is written $\Delta U = Q - W$, where $W$ is the work done by the gas. For a rising parcel, $Q \approx 0$ (no heat in or out) and $W > 0$ (it expands and pushes), so $\Delta U < 0$: its internal energy and temperature drop. Physics 2 and chemistry write the same law as $\Delta U = Q + W$ with $W$ the work done on the gas; there $W$ is negative for an expanding parcel, and the result is the same. Try it in the lab: let the gas expand with no heat added and watch it cool.
A dry parcel lifted from the ground: its temperature (red) falls along the dry rate, about 9.8 °C per km. Press "Lift it" and read its temperature at the top.
✏️ Worked example: Lifting a parcel
A parcel of dry air at 25 °C rises 2 km without reaching saturation. What is its temperature?
It cools 9.8 °C for each km: $2 \times 9.8 = 19.6$ °C.
$25 - 19.6 = 5.4$ °C.
Answer: 5.4 °C
✏️ Worked example: Sinking air
Air at 3 km has a temperature of −5 °C. It sinks to the ground (0 km) without any condensation or evaporation. What is its temperature when it arrives?
Sinking air is squeezed and warms 9.8 °C per km: $3 \times 9.8 = 29.4$ °C.
$-5 + 29.4 = 24.4$ °C. Sinking air arrives warm and dry, which is why sinking air clears the sky.
Answer: 24.4 °C
⚠️ Common mistake
Thinking rising air cools because it gets closer to cold space or farther from the warm ground. A parcel cools because it expands, doing work on the air around it; no heat has to leave it. Check: sinking air warms by the same rate even when it comes down into a cold valley, because it is being squeezed.
Many problems round the dry rate to 10 °C per km to make the arithmetic easy; they say so when they do.