As we have seen, warmer air has a lower density than colder air. This makes it buoyant, making it rise. This is what makes hot air balloons rise. If we take a parcel of warm air and put it into cold air, it will rise. If the warm rising air does not cool and / or the surrounding air does not warm, the parcel of warm air will rise indefinitely.
This is obviously not the case. The rising warm air cools and eventually comes to the same temperature as the surrounding air. It then looses buoyancy and ceases to rise. The way in which the rising air cools is a very important factor in meteorology.
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As the warm air rises it cools adiabatically. This means the air cools only due to pressure drop and expansion, the exchange of heat with the surrounding air is negligible. A rising parcel of air cools by about 10 °C (9.8 °C more precisely) for every kilometer it rises. This value, 9.8 °C/km, is called the dry adiabatic lapse rate. This a very rapid cooling rate, causing dry air to come to the temperature of surrounding air quickly.