What is temperature? This question comes up quite a bit—especially in introductory science courses. The most common answer is something like this:

*Temperature is a measure of the average kinetic energy of the particles in an object. When temperature increases, the motion of these particles also increases.*

It’s not a terrible definition, but it’s not the best either. There are *plenty* of other crazy things about temperature that you should probably know.

### Thermal Energy and Temperature Are Different

If temperature is a measure of the average kinetic energy, shouldn’t thermal energy and temperature be the same thing? No. Thermal energy is the total energy an object has due to the internal motions of its particles. The temperature is related to the *average* kinetic energy—not the total kinetic energy.

Here’s a classic example that you can try at home. Put a piece of cold pizza on top of a sheet of aluminum foil and then stick it in the oven to heat up. After about 10 minutes, the pizza should be nice and hot—the aluminum foil is the approximately the same temperature. You can pull the aluminum foil out with your fingers, but not the pizza. Although the aluminum foil has a high temperature, its low mass means it doesn’t have much thermal energy. Without a lot of thermal energy in the foil, your fingers won’t get burned. Meaning? Thermal energy and temperature are different things.

### More Definitions of Temperature?

You already have one definition from above, but I am going to give you two more definitions. The first one is the historical version. It goes like this:

*Temperature is the quantity that two objects have in common after being in contact for a long time.*

This definition is based on the idea of thermal equilibrium. If you put an aluminum ball into some water, eventually the water and the ball will have the same temperature. They won’t have the same thermal energy, but they will have the same temperature. It’s a very operational definition of temperature—and that’s not a bad thing.

But really, this temperature is the basis of most thermometers. Take your basic mercury or alcohol thermometer (the mercury ones are not so common because—you know, they contain mercury). When you put this thermometer in a liquid or something else, the temperature of the liquid inside the thermometer changes until it is the same as the object. Since both mercury and alcohol expand with an increase in temperature, you can determine the temperature based on this thermal expansion (or contraction). Really, you could say that the thermometer even came before the idea of temperature.

Now for the second definition of temperature. This one is pretty tough, so hold on to something.

*Temperature is the rate that internal energy changes with respect to entropy.*

It’s short, but there’s a lot in there. First, what is entropy? I could try to explain entropy, but this would be a complete new blog post. Instead, you can just check out this very awesome post by Aatish Bhatia in which he explains entropy using sheep. Yes, it’s really good.

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.

You could just plug in a Fahrenheit temperature of -40 and see what you get, but how about a graph instead? Let me plot two lines on the same graph. One line will be the Celsius temperature as a function of Fahrenheit temperature and the other will be Fahrenheit vs. Fahrenheit.

Where do the Fahrenheit and the Celsius lines cross? Yes, at a value of -40. So, the next time you are on Hoth or it is just plain super cold you can say the temperature is -40. When your friend asks “is that in Celsius or Fahrenheit?” just reply “yes.”