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Absolute Zero

Low Temperatures

Introduction

In London temperatures around 0 degrees Celsius are common in the winter. In parts of Scotland temperatures may drop to -20. In Europe and North America temperatures of -40 are common.

At normal room temperatures most substances are solid (e.g. gold, iron, rock), some are liquid (water, mercury) and some are gases (oxygen, carbon dioxide). As temperatures decrease gases turn to liquids and liquids to solids.

Cold and heat are not opposites. Cold is the absence of heat. Heat is energy.

The temperature of something is related to the amount of energy possessed by the particles in the substance (atoms or molecules). This affects how quickly these particles are moving (in a liquid or gas) or vibrating (in a solid). The hotter the substance, the more energy in the molecules and the faster they move or vibrate.

Adding energy to a substance causes its molecules to move faster and this is measured as a rise in temperature. Removing energy causes the molecules to move slower and this is measured as a drop in temperature. If the substance is a gas, the slowing down will eventually bring the molecules together and the substance condenses to a liquid. More cooling and liquids turn to solids as the molecular motions slow down.

On Earth under our atmospheric pressure, water freezes to a solid at 0 degrees Celsius. Sea water (which contains salt) freezes at -2.

Mercury, the only liquid metal at room temperature, solidifies at -39 making thermometers useless below that temperature. At -78 carbon dioxide gas condenses to a solid bypassing the liquid phase, hence its name of dry ice. The coldest temperature ever measured on the surface of the Earth was -90 at a Russian research station in Antarctica.

But it can get colder than this.

Gas Laws

At -183, oxygen condenses to a pale blue liquid, followed at -196 by nitrogen. These two atmospheric gases solidify into ice-like solids at -210 (for nitrogen) and -219 (for oxygen).

By -250 Celsius most substances that we are familiar with on the Earth will be solid. This is colder than any of the major planets in our solar system. Neptune's "surface" temperature, by comparison, is a mild -216 and even ex-planet, Pluto roasts at -223.

Two common gases remain untouched even by the intense cold of -250 Celsius. Hydrogen liquefies at a bone-chilling - 253 becoming solid at -259. At this temperature only helium remains a gas. Its atoms are inactive forming no chemical compounds with any other type of atom and not even wanting to interact with each other. At conditions that we have on Earth, helium liquefies at -269 Celsius, the lowest boiling point of any substance. To solidify helium it must be cooled to -272 and have intense pressure applied.

But how cold can it get. And if cold is the absence of heat, is there a such a thing as a coldest temperature?

To answer that question let us examine the behaviour of gases. Gases obey something called Charles' Law. At a given pressure, if the temperature of a gas is increased its volume also increases in proportion. If the temperature is lowered, the volume decreases, again in proportion. This can be visualised in the diagram below.

Keeping a gas at a constant pressure, as its temperature rises, the molecules move faster and they need more space so the volume increases. If the temperature falls, the molecules slow down and the amount of space needed decreases.

The graph of temperature against volume for a gas is always a straight line. Each type of gas will produce a straight line when temperature and volume are compared but the lines will have different slopes for different gases.

At very low temperatures the gases condense into liquids and stop obeying Charles' Law. However, if we take all these straight lines and extend them down so that they meet the temperature axis, they all meet at the same temperature. The temperature where all these straight lines meet is always MINUS 273.16 degrees Celsius. This is the temperature where any gas would theoretically have a ZERO volume.

Temperature and Molecular Velocity

Let's return to molecular velocities and temperature. There is an equation called the Boltzmann Equation. This tells you the average speed of a molecule or atom for a given temperature. It depends on the mass of the molecule so that for a given temperature a heavy molecule moves slower. On the Earth, at its average temperature, lighter Hydrogen atoms move faster than heavier Oxygen molecules. The hydrogen atoms move so quickly that they can escape from the Earth's gravity. Oxygen molecules are slow enough to remain trapped by Earth's gravity. If the Earth's gravity was weaker (like the Moon's) oxygen would escape. If the Earth was hotter (like the planet Mercury), the oxygen molecules would travel faster and would again escape.

We can take the equation and put a velocity of zero in it. When we do that we are asking the question "at what temperature is the average speed of a particle zero". The answer comes out at MINUS 273.16 degrees Celsius.

Energy

Let's look at the problem from a different angle. Energy comes in different forms carried by waves:

Radio waves have long wavelengths and low energy. Difficult to detect by living organisms.

Infra Red waves are shorter waves with a little more energy. Some reptiles can detect these as heat.

Red visible light is shorter still and has more energy.

Yellow light - shorter waves than red light and more energy.

Blue light - shortest waves of visible light, most energy of visible light.

Ultra Violet rays - shorter waves - higher energy. Can damage skin.

X-Rays - tiny waves - very high energy. Can cause cancers.

Gamma Rays - smallest waves - highest energy. Can kill life.

Every object gives out these waves. Cool objects may emit radio waves. Warmer objects (like mammals) give out infra red rays. When an iron bar is heated it first glows red (the lowest energy of the visible light). Heat it more and it glows orange then yellow. The light being emitted moves to higher energies and smaller wavelengths. Keep heating the iron bar and it turns white hot as all the colours of the rainbow are being emitted. It is the same with stars. Cool stars glow red, hotter stars give out yellow or white light. The very hottest stars are blue. Very hot objects can glow in the ultra violet, x-rays or gamma rays.

There is a simple relationship between the peak wavelength of energy emitted and the temperature of a body. This is called Wien's Law and its graph looks like the image below.

The graph shows that at higher temperatures the peak wavelength of energy emitted gets smaller - hotter objects are bluer.

A wavelength of zero (infinite energy) would be emitted at an infinite temperature. We can use the graph to find out at what temperature the wavelength is infinite or the energy is zero. This temperature is represented by the vertical black line on the left and works out to be (surprise, surprise) MINUS 273.16 degrees Celsius.

The Lowest Temperature

The temperature -273.16 Celsius is clearly something special as it keeps cropping up in all studies of matter and energy.

This temperature is called Absolute Zero and is theoretically the lowest temperature possible. If you try and calculate anything using a lower temperature you end up with negative energies, negative molecular speeds and negative wavelengths.

Scientists have attempted to reach absolute zero. They have always failed. They have managed to get close - very close. The lowest temperature attained in a laboratory is 0.0000000001 degree Celsius above Absolute Zero. This is colder than anywhere in the Universe. The Universe is glowing from the Big bang. It "glows" by emitting very long wave radio waves. The glow of the Universe indicates that even in deep space - far from any star or planet - there is a measurable temperature of approximately -270 degrees Celsius, nearly three degrees above Absolute Zero.

In fact there are good theoretical reasons for not being able to reach Absolute Zero. At Absolute Zero all molecular and atomic motion or vibration should be zero. And that would violate one of the most important principles of Quantum Mechanics (the study of the very small) called the Heisenberg Uncertainty Principle.

It looks like Absolute Zero is a real barrier that cannot be crossed. At least there is a limit to how cold it can get.

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