The Physics Philes, lesson 118: Heat, Temperature, and the Zeroth Law of Thermodynamics

Most of us have spent our entire lives learning about heat and temperature. We know we have to cook some food to make it safe, or store food in an icebox or refrigerator. We know it hurts to touch things that are too hot or two cold. But these measurements of heat and temperature are subjective and imprecise. That won’t do in physics. We need to figure out a way to talk about heat and temperature with precision.

When we talk about heat, we’re really talking about the kinetic energy of a system. The study of heat and how it effects matter is called thermodynamics. In order to study heat, we need a way to measure it.

I mentioned earlier that we intuitively know something about temperature. However, we can’t just use our senses to measure temperature. We need something more objective. Specifically, we can relate temperature to the kinetic energy of a system of molecules. Oof. That sound tough to measure. In just my living room – where I’m sitting right now – there are bunches and bunches of air molecules. Luckily, for our purposes, we don’t have to know the details of a molecular system to define heat and temperature.

Okokok. So how are we supposed to measure temperature, anyway? A thermometer, silly! Think about a simple wall thermometer. You now the kind; with the glass tube and the red liquid. That type of thermometer works because the red liquid expands when heated faster than the glass does and rises up the tube. We think of a thermometer as measuring the temperature of something, a room in this case. Bu that’s not actually what it’s doing. It’s actually measuring the temperature of itself.

What? How? It’s something called thermal equilibrium. To measure the temperature of an object, a thermometer must come in contact with that object. Think about a cup of hot chocolate. If you let it sit in a room-temperature room, the hot chocolate will eventually cool down. What’s going on here? Heat from the hot chocolate is transferred into surrounding environment until the two are the same temperature. When that happens we say the two are in thermal equilibrium. The same thing happens with our thermometer. The thermometer and the room reach thermal equilibrium, and that is the temperature the thermometer reads.

Let’s use thermal equilibrium to analyze three systems called A, B, and C. These three systems are not initially in equilibrium. Let’s surround all three in an insulator that won’t allow for any interaction with anything on the outside; that is, A, B, and C can only interact with each other. Now let’s separate A and B with this type of ideal insulator, but we’ll let C interact with both A and B. After a while, thermal equilibrium will be reached for A and C and B and C. This means that A and B are also in thermal equilibrium with each other.

This might seem obvious, but it’s fundamental to the study of thermodynamics. So fundamental, in fact, that it’s called the Zeroth Law of Thermodynamics. (So called because it was named only after the First and Second Law were named.) Since the reading on a thermometer is stable when the thermometer is in thermal equilibrium, we can say that A, B, and C are the same temperature. The reverse is also true. If two systems have different temperatures, they cannot be in thermal equilibrium.

And with that we have begun our journey into the world of thermodynamics. We’ll talk more about how materials react to heat next week.

Featured image credit: Gerry via Flickr

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