Charles' Law: Gas Volume and Temperature Relationship

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  • 0:05 Charles' Law
  • 2:26 Jacques Charles and…
  • 3:29 Practice Question 1
  • 5:58 Practice Question 2
  • 7:26 Lesson Summary
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Lesson Transcript
Instructor: Kristin Born

Kristin has an M.S. in Chemistry and has taught many at many levels, including introductory and AP Chemistry.

In this lesson, we will discover why the wind blows and what causes a hot air balloon to rise, a couple of the applications of Charles' Law that explain the relationship between the volume and temperature of a gas.

Charles' Law

Johnny Dalton and his family have decided to take a hot air balloon ride over Ideal Island, the place where all gases behave ideally. Remember, ideal gases move rapidly and randomly, they don't lose energy when they collide, and there are no intermolecular forces among particles.

When the molecules in the balloon spread out, the air inside becomes less dense.
Heating Molecules in Balloons

As his family is getting ready to embark on their hot air balloon ride, Johnny notices that the fuel for the balloon is just a simple torch. But, how does a torch lift and move a hot air balloon? As you may recall, heating a gas will increase the speed of the gas particles. After all, temperature is just a measure of the average kinetic energy of the particles. The higher the temperature of the particles, the faster the gas particles will be moving.

According to the kinetic molecular theory, a concept we previously covered, faster gas particles are going to spread out. This causes the gas to take up more space. Well, what happens when fewer particles are taking up the same amount of space? To help you answer this, imagine you have two cubes filled with gas molecules. These cubes are exactly the same size. The first cube has 5 molecules inside it, and the second cube has 50 molecules inside of it. The one holding 50 will have more mass than the one holding 5, and though they are the same volume, their masses are different, so their densities will be different. When particles in a substance spread out and move farther away from each other, the substance becomes less dense.

So, back to our hot air balloon: all the torch is really doing is heating the air inside the balloon, causing the air particles to move faster and spread out, which makes the balloon less dense than the air around it, which causes it to float!

This phenomenon - hot air rising because of a decreased density - is also what causes it to be windy outside. The hot air that rises is replaced by cooler air. As the cooler air moves to replace the warmer air, you feel that movement as wind.

Jacques Charles and Absolute Zero

In the late 1700s, Jacques Charles researched this relationship between the temperature of a gas and its volume. He discovered that if the pressure of a gas is held constant, as that gas is heated, its volume will increase. The reverse of that is also true: cooling a gas will cause its volume to decrease. This relationship is known as Charles' Law.

Lord Kelvin used the law to find absolute zero.
Lord Kelvin Absolute Zero Experiment

This idea is what helped Lord Kelvin discover absolute zero. He measured the volume of several different gases at different temperatures, and he found the same relationship as Charles, but this time, he wondered what would happen if he could cool something enough to make the volume equal to zero. He then extrapolated his data all the way down to a volume of zero and the corresponding temperature at this volume was consistently around -273 degrees Celsius. This temperature became known as absolute zero.

Practice Question 1

Just like the other gas laws, this one can be represented in the form of an equation. V1 / T1 = V2 / T2. Remember, we use the 1s and 2s to indicate the qualities before (1s) and after a change has taken place (2s). Also, the units for volume don't matter as long as they're both the same. The units for temperature must be Kelvins or this equation will not work. Also, remember that this is a theoretical equation because it only works for an ideal gas. Most gases that surround you and me behave very much like ideal gases, so we can use this equation as an approximation for the gases we encounter.

The equation for figuring out volume changes as related to temperature changes.
Charles Law Equation

Let's try a practice question. Say you have a 1.00 L balloon filled with an ideal gas at room temperature (293 Kelvins). If you were to put that balloon in your freezer, which would have a temperature of about 260 Kelvins, what would the new volume of the balloon be?

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