Why do you think temperature is the measure of the average energy of motion of all the particles within a substance?

So, instead of a full explanation of entropy, I will just give some interesting aspects of it. Thermal equilibrium is not a purely energy phenomena. Energy is conserved when two objects reach thermal equilibrium, but it would also be satisfied if one object got hot and the other one became cold. Thermal equilibrium is a statistical process. It just so happens that the most probable outcome for two objects in contact is that they reach the same temperature. The other weird cases (one getting hot and one getting cold) can also technically happen, but their chances are way less than you winning the lottery (and your chance of winning the lottery is essentially zero).

Since temperature is really a statistical quantity, you can't have a temperature of a single particle. So, the next time someone talks about the temperature of a single electron—or worse, the temperature of a photon—maybe you should just walk away.

Which Temperature Scale Is The Best?

There are quite a few temperature scales, but these are three most common: Celsius, Fahrenheit (which I can never spell correctly), and Kelvin. I know that most of the civilized world uses Celsius, but I just have trouble training my brain to think of temperature in this scale. I'm probably too old to change. Also, I always think of this graphic display of the temperature scales which says that 0 degrees Celsius is cold, but at a temperature of 100 degrees Celsius you would be dead (the temperature of boiling water).

How do you calibrate a temperature scale? The Celsius scale is easy. The zero value is at the freezing point of water and the 100 value is at the boiling point. That's fairly easy to reproduce but these values do depend on atmospheric conditions, so it's not a perfect method to calibrate a thermometer. The Kelvin scale is just like the Celsius scale, but it is shifted by 273.15 such that 0 Kelvin (there are no degrees on the Kelvin scale) is equal to 273.15 degrees Celsius. With the Kelvin scale, you don't get negative temperatures—so that's useful in lots of calculations.

But what about the Fahrenheit scale? I think that everyone will agree that it is based on two measurements: the temperature of a human body (around 98 degrees Fahrenheit) and the temperature of salt and ice (0 °F). Actually, this is something that's interesting. If you mix ice and salt (and a little water), the coldest you can get the mixture is zero. That is surprisingly cold and why you use salt-ice mixture to make homemade ice cream.

Still, there does not seem to be complete agreement as to why the human body temperature measures at 98 °F instead of 100 °F. One idea is that the scale is broken into three parts, each of 32 °s, since 32 is the temperature of freezing water. This wouldn't quite work fitting in the human body temperature at 100 °F, but it would be close. Oh well, I guess we won't know until someone invents a time machine.

What Is So Special About -40°?

If you convert -40°F to Celsius, you get -40°C. But the correct answer to the significance of -40° is that it is the temperature on Hoth. OK, if you look at Wookiepedia (the Star Wars Wikia) it says that Hoth gets down to -60°C at night. So, I'm going to guess that maybe during the day it is -40°C (or °F). Anyway, when the MythBusters tested the thermal properties of a tauntaun they used a temperature of -40—so there.

Now for some math. How do you convert from °F to °C? Since both of these are linear temperature scales, I can find a function for the Celsius temperature as a function of Fahrenheit temperature. To do this, I need two data points to make a line. Good thing I already have them—they are the boiling and melting point of water. This gives two x-y points (except x is Fahrenheit temperature and y is the Celsius temperature) that are (32,0) and (212,100). Now I can use these points to find the slope of the line and the point-slope formula to find the equation of the line. I will skip the details (you can do it at home for fun), but I get the following equation.

The dynamics can get more interesting with both differences in amount and temperature. For example, a large pool of cool water can have more thermal energy than a glass of warm water. Why? Because the pool contains more water.

The higher the temperature of a substance, the greater the kinetic energy of the particles!

Temperature

If matter is heated and thus its temperature rises more and more, it can be seen that the particles contained in it move ever faster – be it the relatively free movement of the particles in gases or the oscillation around a rest position in solids.

The temperature of a substance can therefore be regarded as a measure of the velocity of the particles it contains. With a higher temperature and thus higher particle velocity, the kinetic energy of the particles also increases. Therefore the following statement applies :

The higher the temperature of a substance, the greater the kinetic energy of the particles!

More information on the connection between temperature and particle motion, especially for gases, can be found in the article “Kinetic theory of gases“.

Note that particle motion in the context of temperature is always a random motion! The temperature of the cube shown in the animation above would not increase if it were moved at high speed and the individual particles were supposed to be faster. This is because it is no longer a random movement of the individual particles. Rather, the random motion of the particles is superimposed by a directed movement of the cube. Such directed motions have no influence on the random movement of the particles inside the material and thus on the temperature.

Temperature is a measure of the “not directed” kinetic energy of a particle in a substance!

Thermal expansion

As the temperature rises, the higher the particle velocity and the greater the space occupied by the particles. As a result, substances generally expand as the temperature rises. Conversely, this means that a substance generally contracts when cooled. The resulting decrease in volume is connected with an increase in density (see also the animations in the previous section).

The phenomenon that substances generally expand when heated is also known as thermal expansion. This effect is used, for example, in liquid-in-glass thermometers to measure temperatures.

As the temperature rises, the volume of substances usually increases due to the increased space occupied by the particles!

Note that temperature is ultimately a macroscopic quantity (i.e. it can be measured macroscopically), while particle velocity can only be observed on a microscopic scale. Nevertheless, both quantities are connected! For further information see the article “Maxwell-Boltzmann distribution“.

Summary

The following table summarizes the properties of the particles in the various states of matter.

*) Note: With some substances such as e.g. water, a so-called negative thermal expansion (NTE) occurs in a certain temperature range, which leads to an increase in volume despite falling temperature. Read more about this in the article Density anomaly of water.

Brownian motion & diffusion

Since each substance can be assigned a certain temperature, the molecules contained in it are obviously in constant motion. This (random) thermal motion of the particles due to the temperature is also called Brownian motion. Brownian motion can be observed indirectly if an open ink glass is carefully placed in a water.

Even if the water and the ink are macroscopically completely at rest, one will notice after some time a mixing of the water with the ink. The reason for this is the Brownian motion of the particles which causes the water molecules (shown in red) and ink molecules (shown in blue) to mix due to permanent collisions. Differences in concentration are gradually balanced out. Such mixing of different substances is also called diffusion.

Diffusion refers to the mixing of substances due to Brownian motion (striving for diffusion equilibrium)!

The higher the temperature, the faster the diffusion will be, because the stronger the molecule movement and thus the “mixing”.

In a similar way as the mixing of different gases or liquids can be attributed to Brownian motion, a movement of particles can also be observed in solids. Although the particles in solids are usually bound to a certain location by the electrostatic attraction forces, they oscillate more or less strongly around their rest position, depending on the temperature. Due to these oscillations of the particles (shown in red), foreign particles (shown in blue) can move through the atomic structure. The particles are “pushed” through the atomic structure, so to speak.

As the temperature increases, the lattice oscillations increase and the distances between the oscillating particles increase too. This allows diffusing particles to move better through the lattice structure. Again applies: the higher the temperature, the faster the diffusion processes!

Diffusion is a temperature controlled process, i.e. the higher the temperature, the faster the diffusion!