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How It Works
As dry (unsaturated) air rises through the atmosphere, it expands and cools at a predictable rate called the dry adiabatic lapse rate (DALR). The formula Γ = g / cp gives about 9.76 °C per kilometer of altitude gain on Earth. You can also use the related equation T = T₀ − Γh to estimate the air temperature at any altitude.
“Adiabatic” means no heat is exchanged with the surrounding air. This is a good approximation for rising air parcels because air is a poor conductor and the process happens relatively quickly.
Example Problem
The surface temperature at an airport is 25 °C. A pilot needs to know the air temperature at 3,000 m for icing assessment.
- Use the standard DALR: Γ = 9.76 °C/km = 0.00976 °C/m
- T = 25 − 0.00976 × 3000
- T = 25 − 29.28 = −4.28 °C
Since the temperature is below freezing, icing conditions are possible and the pilot would want to check for visible moisture (clouds) at that altitude.
Frequently Asked Questions
What is the dry adiabatic lapse rate value?
On Earth the DALR is approximately 9.76 °C per kilometer (5.4 °F per 1,000 ft). It is derived from g / cp = 9.8 / 1003.5. The value is constant and does not depend on the actual air temperature or humidity.
What is the difference between dry and moist adiabatic lapse rate?
The dry rate (~9.76 °C/km) applies to unsaturated air. Once air reaches its dew point and condensation begins, latent heat release slows the cooling to about 5–6 °C/km — this lower rate is the moist adiabatic lapse rate.
How is the lapse rate used in weather forecasting?
Meteorologists compare the actual temperature profile (environmental lapse rate) with the DALR to assess atmospheric stability. If the environment cools faster than the DALR, the atmosphere is unstable and promotes convection, thunderstorms, and turbulence.
Why does temperature drop with altitude?
Rising air expands because atmospheric pressure decreases with altitude. Expansion does work on the surrounding air, which takes energy from the parcel and lowers its temperature. This is a fundamental thermodynamic process that occurs without any heat exchange with the environment.
Related Calculators
- Ideal Gas Law Calculator — solve for pressure, volume, moles, or temperature using PV = nRT.
- Heat Index Calculator — find apparent temperature from air temperature and humidity.
- Water Vapor Pressure Calculator — calculate vapor pressure at a given temperature.
- Cloud Base Calculator — estimate cloud base altitude from surface temperature and dewpoint.
- Length Converter — convert between meters, feet, and other altitude units.
References:
Holton, James R. 2004. An Introduction to Dynamic Meteorology. Academic Press. 4th ed.
Wallace, John M. and Peter V. Hobbs. 2006. Atmospheric Science: An Introductory Survey. Academic Press. 2nd ed.