Absolute Zero

Absolute zero is the absolute lowest temperature at which matter can theoretically exist.

On the face of it, this is somewhat remarkable.  Why should there be a lower limit?  And how can we know what it is?

There are many textbooks that can give highly rigorous descriptions of why absolute zero is what it is, but presented here is a simple description that at least expresses the fundamental reasoning.  I guess I’d call it a plausibility argument.

Let us start by considering a volume of gas that is warm enough that it is far away from the temperature at which it condenses (as an aside, by adjusting temperatures and/or pressures, all elements can enter gas, liquid or solid phases.  We tend not to ever think of things like the air around us as possibly being liquid or solid because the temperatures and pressures necessary for this to happen are foreign to our experience.  But we are getting off track…)

Let’s get more specific, and imagine a volume of Helium – say a cubic meter – at room temperature.  Helium doesn’t condense into liquid until it’s temperature is about -450°F, so we are certainly not close to that.

Now it turns out that in a highly diffuse gas, there is a relationship between the pressure, the volume and the temperature of the gas.  This relationship is known as the ideal gas law and is expressed as:

P * V = n * R * T

Where P=pressure, V=volume, n=the amount of gas, R=a constant and T=temperature.

The ideal gas law is “ideal” because no real gas precisely obeys the law (because of interactions between particles, rotation of non-monotomic molecules and other factors) but for highly diffuse gases it’s a good proxy.

Because we are looking at a concept rather than trying to determine real numbers, we can drop the n term (which simply corresponds to how much gas we happen to be looking at in this example and which we can simply call “1”) and the R term, which is an unchanging constant.

That tells us that there is a very simple relationship between pressure, volume and temperature:

P * V = T

Now, you may recall that if we extract heat from a substance (such as our gas), the temperature of the substance will decrease (this relationship is quantified as the specific heat of the substance.)

Observe from the above formula that if allow the pressure of our gas to remain constant (in other words, as the gas gets colder, the balloon or whatever is containing it is allowed to shrink so it stays in pressure equilibrium with the surroundings) we find that the change in volume is directly proportional to the temperature:

V proportional to T

Now imagine that we begin extracting heat from our helium and the volume starts decreasing.  We observe the temperature and the volume of the gas at various points as we cool the gas.  This allows us to develop a straight line that shows the relationship between the temperature and the volume (again, we are staying well above the temperatures where the helium atoms significantly interact or threaten to condense out as a liquid.

We observe that if we take our temperature-volume line and extrapolate (extend) it, we will project out to a temperature where the volume of our gas will become zero.  And at temperatures below that, we would have negative volume, which is impossible!  That temperature, the point where the volume of our nearly-ideal gas projects out to be zero, is known as absolute zero.

Heading for Zero

I guess here, I have to make a couple of clarifications.  First of all, there is no real gas that can be driven to absolute zero, because all gases will condense and solidify at low enough temperatures.

Secondly, absolute zero is theoretically the point at which the internal energy of the gas would be at zero.  Although we have not expressly considered it yet, the temperature of a substance reflects the internal energy of the substance.  Therefore, defining absolute zero to zero degrees (in the Rankine and the Kelvin temperature scales) is absolutely logical.  It is the temperature of zero internal energy.

The important take away for our day-to-day energy work is that absolute zero represents the temperature at which the internal energy of matter theoretically reaches zero, and it is the temperature at which an “ideal” gas would reach a volume of zero if it could be cooled to that point.

Note that absolute zero is infrequently used in common energy equations, but it is not unheard of.  Radiant cooling calculations and engine efficiency calculations are two instances where absolute temperature scales are required.

Here’s an interesting question, too:  We have explored reasons why temperatures below absolute zero cannot be achieved, but what about the other end of the scale?  Is there a limit to the maximum possible temperature that matter can reach?  To my knowledge, this question has not been answered.

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