What causes the temperature to decrease with height in the troposphere?
Pressure decrease.
As one climbs in the atmosphere the atmospheric pressure decreases. This is due to there being less atmosphere above you and therefore less mass for gravity to work on. If you are 1000m above the surface of the Earth you would have 1000m less atmosphere on you.
According to Gay-Lussac's law for gases, pressure and temperature are directly proportional. Therefore as the pressure decreases so does the temperature.
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The temperature decreases with height in the troposphere primarily due to the adiabatic cooling effect. This effect occurs as air rises in the atmosphere, it expands due to decreasing atmospheric pressure. Expansion of the air causes it to cool down because energy is required to do work against atmospheric pressure. Additionally, the troposphere is heated primarily from the Earth's surface, so as you move away from the surface, there is less heating from below, contributing to the temperature decrease with height.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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