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Q: Heat is supposed to rise. Why, then, is it colder on top of a mountain than in the valley below?

Numerous readers have written in to say that the answers given to this question in the issue of 16 December 1995 missed out the most important part of the argument. Indeed, they most certainly did. Owing to an oversight during the pre-Christmas rush the key letters which explained how expansion of a gas leads to cooling were omitted, leaving only some which were intended as a supplement to the main answers. We apologise to everyone who may have been misled. This week we explain the effect in detail and add comments on the previously published answers – Ed

A: Air is a poor absorber of sunlight. The Sun heats the Earth which is a better absorber, and the Earth then heats the air close to it. Hot air rises because it is less dense than surrounding cooler air at the same pressure. As it rises, a mass of hot air expands because the ambient pressure is less. This expansion cools the air, so the temperature of a thermal bubble decreases with increasing altitude until it reaches equilibrium.

A: The explanations given previously all miss the fundamental reason, which is based on the gas laws. If air at a low altitude rises it moves into an area of lower pressure. If there is no heat transfer its temperature falls. The air expands as it rises and this expansion does work against the surrounding air, taking energy from the rising air and cooling it.

So the dynamic equilibrium condition in the atmosphere is one of falling temperature with increasing altitude.

A: This phenomenon is explained by what is termed adiabatic expansion. Think of a balloon inflated at sea level which is then carried up a high mountain. As the atmospheric pressure drops, the balloon will expand because a given mass of gas will occupy a larger volume if it is at a lower pressure.

The work that expands the balloon against its elasticity and the pressure of the gas outside comes from the air inside it. As this air is allowed to expand it does work. This energy in turn is derived from the thermal energy (motion) of the air molecules inside the balloon and because of the work that it is doing the air cools.

This phenomenon will cool the air by approximately 9°C per kilometre of altitude. Therefore air at 20° C at sea level would be in neutral equilibrium with air at 11 °C at 1 kilometre altitude. This is close to the temperature gradient that is seen in the lower 8 kilometres of our atmosphere, above which other effects dominate.

A: The air pressure at any point is a measure of how much air lies above that point, so air pressure decreases with height. As air pressure decreases, temperature decreases; so temperatures will nearly always be colder on the top of a mountain than in the valley below.

The exception is when inversions occur, but this does not alter the basic premise. If the air is heated at the Earth’s surface, it will rise because it is less dense than the air around it – the warmer air is, the less dense it is.

As the air rises, its pressure decreases, and thus it cools, so again the air on the mountain will be cooler than in the valley. This is a simplification of the many processes that are happening in the atmosphere, but even so it is the most important.

A: To describe the atmosphere as being like the skin of an onion and therefore having more volume in its outer, as compared to its inner layers, is conceptually wrong.

As the Earth is nearly 13 000 kilometres in diameter and the top of the troposphere is only 13 kilometres above the surface, a more realistic analogy is that the parts of the atmosphere are more like the skin of an orange rather than the layers of an onion. Thus the volume of air at a given height does not increase significantly with altitude and so this effect is insignificant in determining temperature drops.

To these fuller explanations might be added the point made by Rosemary Gray in the earlier answers that temperatures do start to rise again much higher up in the atmosphere – Ed.

This week’s questions

Simply yellow: I read that this autumn (1995), the colour of the leaves on deciduous trees was predominantly yellow rather than red. Is there some seasonal effect that influences the colour of the pigments in leaves after the chlorophyll has broken down?

Helen Gavin, Reading, Berkshire

Flat stoned: While walking down a stony beach and skimming some stones into the sea, I noticed that the flattest pebbles (and the best ones to use for skimming) tended to accumulate at the top of the beach, furthest from the sea. Why is this?

Matthew Richardson, Edinburgh

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