If cold air is denser than hot air, then why does the temperature decrease as the altitude rises?

The relationship between air density and temperature, and how temperature decreases with altitude, can be explained by understanding atmospheric physics.

Air Density and Temperature

• Density and Temperature Relationship: Cold air is denser than hot air because the molecules in cold air are closer together, resulting in a higher mass per unit volume. Conversely, hot air is less dense because its molecules are farther apart, reducing the mass per unit volume13.
• Air Density Formula: The density of air ((\rho)) can be calculated using the formula (\rho = \frac{p}{R \cdot T}), where (p) is pressure, (R) is the gas constant, and (T) is temperature in Kelvin1.

Temperature Decrease with Altitude

• Pressure Decrease: As altitude increases, atmospheric pressure decreases because there is less air above to exert pressure25.
• Expansion and Cooling: When air rises, it expands into regions of lower pressure. This expansion requires energy, which is drawn from the thermal energy of the air, causing it to cool4.
• Lapse Rate: The standard lapse rate indicates that temperature decreases by about 6.5°C for every 1000 meters gained in altitude5. This cooling effect is why it is generally colder at higher elevations.

In summary, while cold air is denser than hot air, the temperature decrease with altitude is primarily due to the expansion and cooling of air as it rises into lower-pressure regions, not because cold air rises to higher altitudes. Instead, the rising air itself cools as it expands.