 Absolute Zero and the Conquest of Cold
Looks to be an interesting investigation into the understanding of cold - is it just the absence of heat? - and into the attempts to achieve ever lower temperatures The refrigerator and the universe
Those of you who want a substantial introduction to thermodynamics, but without going into the technicalities, should take a look at this book
My Review of The refrigerator and the universe Four Laws that drive the Universe
P W Atkins' latest book, in which he gives a gentle introduction to the laws of thermodynamics, including a discussion of why we can't reach absolute zero
My Review of Four Laws that drive the Universe Frost patterns on a screened window
Artist: George F. Mobley

## Can we reach absolute zero?

The Absolute Zero of temperature is thought of as an unattainable goal. Whatever the design and power of your refrigerator, it will never be able to reach this limit. However when I began to look at the arguments for this, I found them unconvincing. See what you think...

### Refrigeration

The science of thermodynamics started with the question of the efficiency of steam engines. It was realised that to extract useful work it was necessary to have a hot source (burning coal) and a cold sink (the surroundings), and that useful energy could be extracted in the process of transferring heat from the hot source to the cold sink. However, such idealised heat engines can also be thought of as working in reverse, in which case there is an input of useful work and the result is to transfer heat from a cold place to a hotter one - this is how a refrigerator works.

If TH is the temperature of the environment and TC that of the cold object then a perfect refrigerator will use (TH/TC-1) units of energy for each unit of energy extracted from the cold object. So if we consider matter with a heat capacity of C Joules/Kelvin then the work required to decrease the temperature of the object down to T0, with the environment at TH is,
 TH T0
(
 TH T
-1)CdT
Hence if C is constant, then this tends to infinity as T tends to 0, implying that it would take an infinite amount of energy to cool a sample down to absolute zero - an unattainable limit!

### Efficient energy storage

The above ideas got me thinking. If you used energy to cool an object down then in theory you could get this energy back by using the object as the cold sink for a heat engine. This might be used as a way of storing energy. Indeed liquid nitrogen has been used to power an engine, but it own produces about 5% of the energy of the same weight of gasoline - although it has its uses in safety critical situations. If you do the sums for liquid helium it doesn't work out much better. But if there's the possibility to store an infinite amount of energy in a finite amount of matter then you would think that there would be plenty of useful applications - for instance getting into orbit.

### Unfortunately there's a catch

The trouble is that the above calculations assume a constant heat capacity over temperature, and heat capacity is certainly not constant when you decrease the temperature - it drops to zero. If you look at the theoretical energy required to cool something to absolute zero you then get a finite answer. Indeed this enables us to define absolute zero as the temperature at which everything has zero entropy - the Third Law of Thermodynamics. The third law is often said to mean that absolute zero is unattainable, but I don't see how to deduce this. True, it might seem that you could use an object at absolute zero as a cold sink for a heat engine, and thus generate useful energy without increasing the temperature of the cold sink, but in fact the increase in temperature isn't 0, it's 0/0, implying we need a new way of looking at it.

### Quantum considerations

In the case of a normal solid, the temperature is related to the atoms vibrating with respect to each other. However, quantum theory tells us that vibration of the atoms is quantised. Cooling in these circumstances is a case of removing the quanta of energy from the system, and reaching absolute zero means removing the last quantum of energy. This doesn't seem that simple, at least using technology we can think of today, but I'm not sure that it's theoretically impossible. Of course low temperature quantum systems lead to things such as Bose-Einstein condensates, where a collection of atoms are cooled so much that they all adopt the same quantum state, and it's harder to understand the concept of temperature to such a state.