Thermal Equilibrium

Any object that has a constant temperature is in a state of thermal equilibrium. This means the rate at which energy is transferred to the object is exactly equal to the rate at which energy is transferred from the object. In the context of electromagnetic radiation, we can state that the rate at which the object absorbs energy is exactly the same as the rate at which it emits energy.

This is one of the fundamental principles of physics as it explains why objects heat up or cool down. An object will heat up if it gains more energy than it is capable of losing in the same amount of time. Similarly, an object will cool down if it loses more energy than it gains in the same amount of time.

There is a separate post about the conversion of thermal energy into electromagnetic energy (the emission of infra-red radiation by hot objects) which you can read here.

Let’s look at this in practice using some isolated objects where we only need to think about absorbed and radiated electromagnetic energy – leaving aside any issues to do with conduction or convection. This is especially important for those of you who are doing Higher Tier.

First, let’s think about the International Space Station in orbit above the Earth. To stay at a constant temperature that will support human life, the ISS must ensure that it does not absorb more heat (infra-red radiation) than it emits when it is in direct sunlight. Similarly, it must not lose too much heat when in the Earth’s shadow.

Sadly, when the ISS is in direct sunlight its temperature could easily rise above the boiling point of water and when in shadow the temperature could drop to more than 100 ‘C below the freezing point of water! Clearly it is a huge challenge to maintain the temperature of the ISS within a safe range for human life. (You can read more about this challenge on an old NASA web-page here.)

A similar situation applies on the Moon, where the sunlit side of the moon is at a temperature above the boiling point of water and the dark side would be cold enough to condense oxygen gas into a liquid. Interestingly, at a depth of just 1 m below the lunar surface there is almost no temperature variation owing the the “soil” (regolith) having a very low thermal conductivity. So future Lunar bases might well be underground or covered under at least a metre of regolith!

(There is a really interesting NASA paper about this, dated 1993, which you can download here: pages 5-7 contain the most relevant information for our purposes.)

What about the Earth? Why don’t we have the same problem of really hot (boiling water) days and freezing (almost cold enough to turn oxygen into liquid) nights? The answer is that our atmosphere acts like a blanket to keep us warm at night while clouds act as reflectors to return some of the Sun’s heat back into space before it is absorbed.

The Sun’s energy that is absorbed warms-up the Earth. This in turn makes the Earth radiate its own heat that travels through the atmosphere before it is released into space. Unfortunately, human activity has changed the composition of the atmosphere and made it less transparent to the infra-red radiation that the Earth is trying to lose. This in turn results in heat becoming trapped and the Earth’s temperature rising – the effect that we call Global Warming.

In getting hotter, the Earth is simply trying to reach a new thermal equilibrium. We know that hotter objects radiate energy faster than cooler objects and the Earth is simply echoing that principle. If the same amount of sunlight is still arriving at the Earth’s surface but more energy is being retained (stored by carbon dioxide gas in the atmosphere) then the Earth will not radiate as much energy as it is receiving. This means the Earth will heat up until it achieves the necessary rate of radiating energy (after allowing for the loss of radiation due energy that is retained by carbon dioxide and other gases) that again matches the original rate of absorbing energy.

At this point the Earth may simply reach a new thermal equilibrium that gives us a new average temperature. Of course the higher average temperature may have other effects, such as melting some of the polar ice. Solid ice is white and reflects a lot of energy whereas melted ice (water) does not have the same reflective properties. So the Earth could then need to achieve yet another new energy balance due to more energy being absorbed. This is clearly a very complicated (and very exciting) area of physics that some of you may wish to explore in your future careers.