The temperature decreases with height in the troposphere due to the following reasons:
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Decrease in atmospheric pressure: As one climbs in the atmosphere, the atmospheric pressure decreases. This is due to there being less atmosphere above and therefore less mass for gravity to work on. According to Gay-Lussacs law for gases, pressure and temperature are directly proportional. Therefore, as the pressure decreases, so does the temperature.
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Absorption and re-emission of incoming solar radiation: The troposphere is warmed from below through absorption and re-emission of incoming solar radiation by the Earths surface. The warmest temperatures in the troposphere are near the surface with the coldest temperatures being at the top of the troposphere. Although sunlight comes from the top to the bottom of the atmosphere, the troposphere is primarily heated from the bottom.
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Adiabatic cooling: Since the temperature decreases with height in the troposphere, it can be easy for air to rise vertically since cooler air over warmer air is an unstable situation. When air rises, it cools adiabatically. This is another reason the temperatures are colder aloft than at the surface. For air to rise to a higher elevation, it must cool. Air density and pressure are highest at the surface.
In summary, the decrease in atmospheric pressure, absorption and re-emission of incoming solar radiation, and adiabatic cooling are the main reasons why the temperature decreases with height in the troposphere.