Article curated by Grace Mason-Jarrett
Energy can neither be created nor destroyed; it can only be changed from one form to another. This famous axiom was stated by Einstein, but what does it actually mean? You’ve probably noticed that wearing black or darker clothing on a hot day makes you feel hotter than if you wore light or white coloured clothing – thermodynamics can explain this. The study of thermodynamics is one which looks at how energy changes its own form, from thermal energy to kinetic energy for example, and how energy is absorbed and interacts with different materials. It explains why ice floats on water, and what happens in changes of state – from gas to liquid to solid. Thanks to thermodynamics, we have also found a number of in-between states, plasmas and supercooled liquids, which have properties not always found in everyday life.
Thermodynamics is successful at explaining many things we experience, but every now and then a paradox will pop up and baffle us, or someone will spot an event which no one has an explanation for yet.
Paradoxes and peculiar effects
You may have heard that glass is actually a liquid – it just moves really slowly. This is an oversimplification but not a bad way to explain what actually defines a material as a glass. A glass is any material which has been formed by a liquid becoming more and more viscous until it appears to be completely solid, but there is no change in the bonds between molecules or the molecules themselves. Polymers are much better at forming glasses than other materials. This is different to other liquid-solid phase changes, for example water to ice, where the physical structure of the material changes. The glass transition, as it is known, is a reversible process which can happen at a range of temperatures provided the pressure is right so that the material is still liquid.
The collection of things we can measure about something make up its “state” - the temperature, pressure, and so on. One of these terms, Entropy, describes how much disorder there is within the material. While not a completely accurate analogy, you can think of this as how ‘messy’ the molecules are. The third law of Thermodynamics states that at absolute zero (-273 degrees Celsius) the entropy of a system is zero and the material is now in a perfect crystal state. This means, in short, that the system is as perfectly frozen as it’s going to get, and it can’t have any less energy than it has at absolute zero.
The Kauzmann paradox comes about because it has been noticed that the difference in entropy between the liquid and the solid states of the glass transition becomes zero at a specific temperature called the Kauzmann temperature. The Kauzmann temperature is lower than the material’s freezing point and so it requires the material to be supercooled – this means it has to be brought to a temperature below its freezing point without actually freezing. If we lower the temperature even more past the Kauzmann temperature, the difference between the two states becomes negative. This means that the entropy of the glass transition material is less than the entropy of the same material in its crystal phase, so the entropy at absolute zero would be less than zero – a direct violation of the third law of thermodynamics!
Despite there being several strong ideas about what’s going on here, scientists cannot agree on the cause of such defiance and so the paradox remains a mystery.
Erasto Mpemba made his name known by bringing the attention of scientists to a problem which has been left unsolved since Aristotle first noticed it over 2,000 years ago. Hot liquids, under certain specific conditions, freeze faster than cold liquids – but why? It doesn’t seem to make any sense at first, since a hotter liquid is much further-away from being frozen than a cold one – at least in terms of temperatures. So, what’s going on? There are a number of ideas floating about – for example hot liquids evaporate more quickly, leaving a smaller volume of liquid left to be frozen. Another idea entertains the fact that hotter liquids have lower densities and so convection currents are more active. Since convection currents transfer thermal energy from hotter to cooler areas the heat will be lost quicker and so the hot liquid cools faster than the cold one. None of these events could have a big enough effect on the liquid to account for the Mpemba effect though, so there must be something else at fault here.
By observing what happens when you try to supercool hotter and colder liquids, researchers have found that liquids with a higher starting temperature are less able to supercool – i.e. more likely to freeze below their freezing temperature. This doesn’t actually help to answer the problem of the Mpemba effect; conversely it adds more questions to the mix. Despite claims that the Mpemba effect has been solved, there is not enough conclusive evidence for any definite resolution to this problem.
Perhaps the vaguest thing about this effect though is its definition – scientists cannot agree on whether the measurements should be until the liquid is entirely solid, or until it reaches its freezing temperature. Until this issue has been resolved we cannot develop the understanding further.
Learn more about The Mpemba Effect.
Water isn't the only liquid whose freezing behaviour is confusing. Surface freezing is an uncommon phenomenon where long-range crystalline order appears in a substance first at the near-surface layer of a liquid. It has only been experimentally found in chain-structured molecules such as alkanes. Furthermore, in intermediate chain length alkanes (between 16 and 50 carbon atoms) this happens at a temperature 3 degrees higher than the equilibrium melting temperature. This is the temperature at which an infinite stack of crystals in a homogeneous substance will melt. There is no consensus yet on why only chain-structured molecules should show surface freezing, and it is very little understood why the length of the alkane chain should show this disparity with the equilibrium melting temperature.
Problems with thermal equilibrium
Using ultracold atoms trapped in light crystals, a novel state of matter was discovered in 2015 - a many body localised state - that never thermalises, despite the presence of interactions. In this peculiar insulating state the system retains a quantum memory of its initial quantum state, even for long times.
When we mix hot and cold water, through the processes of thermodynamics, we end up with warm water. But this is not the case when it comes to these crystals. Although this field has been of interest before, observational studies are lacking, so hopefully we will gain more of an insight into this phenomenon and its implications for quantum information science.
The scientists behind the discovery of this state raised the question
what if the particles were trapped in a rigid lattice that does not vibrate? Would the system then remain localized at elevated temperature and fail to attain thermal equilibrium? This is still a fundamental open question.
Planets should settle down into a state of thermal equilibrium, whereby the total energy they emit into space matches the energy being absorbed from the Sun. Any other condition would lead to either the planet's temperature rapidly spiralling upwards (and so increasing the energy output until it matched) or dropping (and so reducing the energy output).
However, it seems the gas giants Jupiter, Saturn and Neptune don't want to obey this particular law, since they all emit more heat than they receive - which means they must have some form of internal heat source. The emitted thermal energy exceeds the absorbed solar energy by 57%, 80%, and 157% for Jupiter, Saturn, and Neptune, respectively . We don't know what the heat source is, though one option is a "georeactor" whereby nuclear reactions are taking place in the core of the planet. We know that the Earth, in its past, has had such reactors within it too.
Learn more about Energy imbalance of the giant planets.
Sometimes, the same molecular combination of elements will form different crystal structures – resulting in different materials that will react in different ways to pressures and temperatures and other such external variables, despite being having the same elemental ingredients! This is known as polymorphism, and is one of the biggest mysteries in thermodynamics. Factors such as the solvent used, or even the way in which the solution was stirred before forming a crystal, are known to affect which polymorph forms. Polymorphs of the same solution can be different in obvious ways such as colour or transparency, or subtly different in the way they react to external factors.
Very little is understood about the exact mechanism of polymorphism, we know things can change the stakes – but why? There’s a theory-based rule, which appears to work sometimes, developed by a Baltic German chemist called Wilhelm Ostwald stating that it is the least stable polymorph which will form first. Yet this rule is vague in its explanation of why this might be. Ostwald’s rule isn’t widely accepted by scientists as a rule of thumb, but there are very few other candidates for explaining polymorphism out there.
Why is water most dense at 4 degrees Celsius?
It seems that despite years of work on water, hydrogen bonding, and water clusters, no one has quite yet managed to answer the question: why 4 degrees exactly? We know that hydrogen bonding is responsible for water's odd behaviour (in particular, that it expands when it freezes) but, as far as we can determine, no one has yet produced a model that exactly explains why maximum density should occur at 4 degrees Celsius rather than any other temperature.
Learn more about Why is water most dense at 4 degrees Celsius?.
Thermodynamics: the close relative of Gravity?
Something lightly touched upon in a paper written by theoretical physicist and string theorist, Erik Verlinde – there could possibly be a link between gravity and thermodynamics! In his own words;
The universal nature of gravity is also demonstrated by the fact that its basic equations closely resemble the laws of thermodynamics and hydrodynamics. Does this mean thermodynamics could explain gravity too? The exciting thing about the symmetry in the equations, is that it could be pointing toward a unification theory which encompasses all aspects of physics and explains everything with one equation.
Currently, there is no clear explanation for why gravity and thermodynamic theory might resemble each other so closely - then again, one might not be needed as this could just be a coincidence.
Learn more about Gravity and Thermodynamics.
This article was written by the Things We Don’t Know editorial team, with contributions from Ed Trollope, Freya Leask, Kat Day, and Holly Godwin.
This article was first published on 2015-08-27 and was last updated on 2018-01-21.
why don’t all references have links?
 Schreiber, M., et al., (2015) Observation of many-body localization of interacting fermions in a quasirandom optical lattice Science 349(6250):842-845 DOI: 10.1126/science.aaa7432
 Li, L., et al., (2011) The global energy balance of Titan Geophysical Research Letters 38:L23201 DOI: 10.1029/2011GL050053
 Conrath, B. J., R. A. Hanel, and R. E. Samuelson (1989), Thermal structure and heat balance of the outer planets, in Origin and Evolution of Planetary and Satellite Atmospheres, edited by S. K. Atreya, J. B. Pollack, and M. S. Matthews, pp. 513–538, Univ. of Ariz. Press, Tucson.
 Ingersoll, A. P., (1990) Atmospheric dynamics of the outer planets. Science 248:308-315 DOI: 10.1126/science.248.4953.308
 Verlinde, E., (2011) On the origin of gravity and the laws of Newton Journal of High Energy Physics 2011:29 DOI: 10.1007/JHEP04(2011)029
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