# Phase diagrams

Everybody knows that water freezes at 0°C and melts at 100°C, right?

Except that’s not always true. The melting point and boiling point of water depends on the pressure of the water: water only freezes at 0°C and melts at 100°C when it’s at standard atmospheric pressure: 101325 pascals. For example, you cannot make a good cup of tea at the peak of Mount Everest because the pressure is lower there and therefore water boils at a lower temperature (around 71°C), lower than the temperature required to properly release the flavour from the tea.

Information about a substance’s melting and boiling points at different pressures can be represented on a phase diagram. The phase diagram for water is shown below:

From the diagram, we can see that at pressures below around 600 Pa, water transforms from a solid to a gas without passing through a liquid phase. This is a process known as sublimation, and is most well-known from the carbon dioxide “fog” created when dry ice is placed into hot water. We can also see the triple point, a combination of temperature and pressure (0.01°C and 611.73 Pa) at which ice can exist in all three states simultaneously.

View post on imgur.com

Cyclohexane at its triple point boiling and freezing simultaneously.

At higher pressures, the melting point of water changes. Water can remain as solid ice up to temperatures of more than 300°C when the pressure is above ten gigapascals. What is also interesting is the different types of solid water that are formed at different pressures and temperatures.

# Why Can’t We Get to Absolute Zero?

The temperature of a substance is a measure of the average kinetic energy of the particles in that substance. As the average kinetic energy of the particles increases (i.e. they move faster), the temperature of that substance increases.

Some of the particles in a very hot substance will be moving slower than some of the particles in a very cold substance, but the average speed of the particles in a hot substance will be faster than the average speed of the particles in a cold substance. The number of particles at each speed in a gas is governed by something called a Maxwell-Boltzmann distribution, and is shown for air in the graph below:

The average speed for particles of air* at 0°C is around 400 metres per second, for air at 100°C it is about 460?m/s and for air at 1000°C it is about 860?m/s. (Note also that at 1000°C there is far more variation in the speeds of particles than for air at 0°C.) At absolute zero, the coldest possible temperature, particles have a minimum of kinetic energy, and therefore the lowest possible speed. (They cannot have a kinetic energy of zero and actually be stationary because of something called degeneracy pressure.)

So why can’t we cool something all the way to absolute zero?

For something to cool down, it has to lose thermal energy. In order to lose thermal energy, this thermal energy has to go somewhere, and thermal energy only ever moves from hot to cold.** For example: a warm can of drink placed into a cold fridge loses thermal energy to its surroundings until it reaches the same temperature as the fridge’s interior.

Therefore, in order to bring something to absolute zero it would have to be surrounded by something that is colder than absolute zero, and this is impossible: hence you cannot achieve a temperature of absolute zero.

The closest we’ve ever got to absolute zero is less than 100 picokelvin, or 100 trillionths of a degree above absolute zero at the Low Temperature Lab at the University of Aalto in Finland. Interestingly though, it would be possible for something to feel colder than absolute zero due to wind chill.

* Obviously air is made up of different gases travelling at different speeds, so this is an average, weighted by the masses and prevalences of the different gases that make up air.

** It would actually be more accurate to say that the net movement of thermal energy is always from hot to cold. Some energy may go from cold to hot, but more will always go in the opposite “direction”.

# Galileo thermometer

Like most physicists, I have a soft spot for Galileo thermometers.

A Galileo thermometer* works because the density of water changes as its temperature changes. The mass of a substance remains constant as it is heated (because the number of atoms doesn’t change) but because those atoms move faster the volume increases and therefore the density decreases, as shown in the graph for water below.

As the water inside the thermometer is heated by its environment its density decreases and the more dense bubbles, that represent lower temperatures, are then more dense than the surrounding fluid and therefore sink. The Galileo thermometer is read by reading the temperature tag of the bubble closest to the middle of the cylinder.

The density of the bubbles inside the thermometer is set by altering the size of the metal tags attached to them: the bubbles that represent higher temperatures have smaller tags and therefore lower densities. (The overall density of the bubble does not change as it is heated because the overall density of the bubble depends only on its overall mass and overall volume, and as the liquid inside a bubble expands it merely compresses the air inside that bubble.)

* Not actually invented by Galileo, but by a group that included one of his students.

# Colour temperature and f.lux

All objects emit electromagnetic radiation, and the type and amount of radiation emitted depends on the object’s temperature. The hotter the object, the higher the energy of the emitted EM radiation: a cold object will emit radio waves and as temperature increases, microwaves, infrared, visible light, ultraviolet, x-rays and gamma rays.

The surface of the Sun is about 6000K which means that it produces light right across the spectrum, peaking in the green. It is this green coloured light that humans (and other land mammals with colour vision) are most sensitive to – you have twice as many green-sensitive cones as red- and blue-sensitive ones.

A standard incandescent filament lightbulb uses a titanium filament at a temperature of 1500K. This is significantly colder than the Sun which means less higher-energy green and blue light is emitted, leading to an overall yellow colour. Flourescent lighbulbs do not work in the same way so their colour temperature is adjusted by altering the mix of phosphors inside the bulb.

Left to right: simulated 6500K, 2000K, 2650K and 3000K compact fluorescent bulbs

I spend a lot of time in front of a computer screen; something that is not good for the eyes. I have a program called f.lux installed on my laptop that adjusts the colour temperature of my monitor automatically throughout the day; during the daytime the colour temperature is 6500K, after sunset it drops slowly to 3400K. This helps to reduce eyestrain and maintain circadian rhythms.