# How a System Approaches Thermal Equilibrium

Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

After reading this lesson, you'll understand the processes that are happening at the atomic level when you turn on your heater in the winter and when you turn on your air conditioner in the summer.

## Thermal Equilibrium

Think back to when you turned on either the heater or the air conditioner. What happened to the inside of your house after a while? If you had your heater on, it got warmer and if you had your air conditioner on, it got colder. How did this happen? It's all a part of the thermal equilibrium process which says that when you have a system of several connected objects of different temperatures, they will all reach the same temperature. So, when you turn on your heater and it blows hot air into your home, this introduces an object that's warmer than the air inside your home. This causes the thermal equilibrium process to begin and the result is a warmer home for you.

## Two Temperatures

This very interesting process all begins with objects of two or more different temperatures. For example, having hot coffee on a chilly morning. Your coffee is obviously warmer, temperature-wise, than the chilly morning air.

If you leave your hot coffee out in the chilly morning air, what happens? You'll see steam coming off the top of your hot coffee and mixing with the morning air. And soon enough, your hot coffee isn't hot anymore. It's now warm. A little bit later, your warm coffee is no longer warm, but lukewarm. And then it becomes cool and finally, it becomes the same temperature as the chilly morning air.

## Atomic Interactions

You know that examples like the one with hot coffee happen all the time, and you don't question it. But do you know what is happening at the atomic level?

If you zoom in (a lot) to the surface of your hot coffee, you'll actually begin to see a whole lot of activity. You'll see the atoms of the hot coffee bouncing around like crazy. Picture in your head a whole lot of balls being bounced around in a closed room. This crazy bouncing around transfers to the air touching the surface of the hot coffee. The atoms of the air here are also bouncing around like crazy. How crazy or how fast this bouncing around is happening is also referred to as thermal energy.

Looking at the cooler morning air, you notice that the atomic balls are moving slower, much slower in fact. As you look around, you notice something interesting happening with the atoms where the cool air meets the hot coffee. You notice that the crazy bouncing hot atoms are colliding with the slower moving cold atoms. This causes the slower moving atoms to speed up. As you keep watching, you see more and more atoms of the cold morning air begin to speed up as they are hit with the crazy atoms from the hot coffee. As the hot coffee atoms hit the cool air atoms, they lose some speed. This transfer of energy from the hot atoms to the cooler atoms is what causes your hot coffee to turn cold.

You might be wondering why the hot coffee got cold but not the cold morning air. That's because the coffee is so much smaller than the cold morning air. It did warm up the surrounding air, but because there was so much more cold air, the temperature soon equalized to that of the cooler morning air. Also, because heat transfers when a high-energy atom hits a low-energy atom, the bigger the temperature difference, the faster the heat transfer. When two objects have temperatures that are similar, it takes longer for the temperatures to equalize and reach thermal equilibrium.

## From Warm to Cold

Since heat transfers when a hot high-energy atom hits a cooler low-energy atom, thermal equilibrium is usually reached when enough energy from the hot or warm object has been released to the cooler object. So your heat energy or heat transfer is usually from hot to cold.

This is why when you open your front door on a really hot summer day, you'll feel the hot air just rush in. The high-energy bouncing atoms from the hot air is being transferred to the low-energy bouncing atoms of your air conditioned home. Now, this air by the door is also hot. Once you close the door, it will begin to cool down since there is more cool air than there is warm air in your home.

## The Formula

There is a formula that tells you just how much heat energy is required to raise a particular object by a certain amount of degrees.

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