# 3 ways to prove Charles's law

Charles's law states that the volume of an ideal gas changes proportionally to the temperature of that gas, as long as the pressure and the amount of gas present are kept constant. The equation of Charles's law can be expressed in the form V1/ T1= V2/ T2. In other words, if you fill a balloon with air, it will shrink (decrease in volume) if you cool it, and expand (take up more volume) if you heat it. This is because the air inside the balloon, which is a gas, occupies a smaller volume when it is cold and a greater volume when it is hot.

## Steps

### Method 1 of 3: Prove Charles's Law with an Inflated Balloon

#### Step 1. Add hot water to a beaker or other similar container

You should leave room to also put a balloon in the container. Usually 100 ml of water in a 1000 ml (1 L) glass is sufficient. Be careful not to splash hot water, because you could hurt yourself or someone else.

#### Step 2. Fill a balloon with air

Blow the balloon with your mouth or use an air pump to fill it. Do not overfill the balloon: you must leave room for the gas inside it to expand. It is better to use a party balloon than a water balloon. This type of balloon has less risk of exploding. If you are putting the balloon in the container, be careful not to inflate it so much that it will not fit through the opening of the container afterwards.

#### Step 3. Wrap a string around the widest part of the balloon

By surrounding the balloon with a string, you can get an exact measurement of how big the balloon is at the start. Mark or cut the string at the widest part of the balloon. Then remove it from the balloon and measure it with a ruler. That measurement is the original circumference of the balloon. Later, when the air warms up, you can compare it to the size of the balloon.

#### Step 4. Place the balloon in the container

This will allow you to heat the water to transfer the hot air into the balloon. If the balloon does not fit in the container, another option is to place it on top of the container. The heat transfer will be less efficient, but it will still have the same effect on the balloon.

#### Step 5. Watch the balloon grow

The increase in temperature will force the air to increase in size and therefore the balloon will end up expanding. It will look like the balloon is growing or inflating further inside the container. Use another string to measure the circumference of the balloon as you heat it. Now, you can compare that measurement to the original measurement of the balloon.

### Don't let the balloon expand too much because it could explode

#### Step 6. Put the balloon in the freezer

Now that you heated the balloon and it expanded, you will see that when you take it away from the heat it will deflate. In order to observe this effect, you will have to remove the balloon from the heat source (the boiling water container) and take it to a cold environment. You should leave the balloon in the freezer for at least a couple of hours before removing it.

#### Step 7. Look at the size of the balloon

When you remove the balloon from the freezer, immediately measure the circumference with another piece of string. In this way, you can compare it with the first two measurements. Not only will it be smaller than when it was in the hot container, but it will be smaller than when you just inflated it. This is because you removed the heat from the gas that was inside the balloon, which caused the gas (and consequently the balloon as well) to reduce in volume.

### Method 2 of 3: Prove Charles's Law by Expanding and Contracting a Balloon

#### Step 1. Put a small amount of water in an Erlenmeyer flask

You don't need to fill the flask. The less water you add, the faster the water will boil. However, make sure to add enough water so that it also doesn't boil too fast and ends up evaporating. About 75 ml will be enough.

#### Step 2. Place the flask on a hot plate or burner

This will be the heat source with which you are going to heat the water. Make sure to heat it to the boiling point. This will cause the air to expand towards the top of the flask and will also generate the water vapor with which you are going to fill the balloon.

#### Step 3. Place the open end of a balloon over the mouth of the flask

Remember that the flask will be heating up. It is best to wear gloves to avoid burning your hands while placing the balloon over the mouth of the flask. Make sure to lower the balloon down the neck of the flask far enough so that the balloon doesn't come off easily.

### It may be easier and safer to put the balloon in the flask before heating the water

#### Step 4. Watch the balloon expand

If you secure the balloon over the top of the flask, it will be sealed and you will only allow the air to expand inside the balloon. This expansion of air inside the balloon will cause the balloon to expand as well. Don't let the balloon get so big that it ends up popping!

#### Step 5. Now move the flask to a container with ice

Take a container and put water and ice in it. This is the easiest and fastest way to cool the contents of the flask. Wear gloves to move the flask from the heat source to the ice container.

#### Step 6. Observe the suction effect on the balloon

Rapid cooling of the flask and balloon will cause the volume of the gas to decrease. As the volume of the gas decreases, the volume of the balloon will also decrease, and therefore it will end up shrinking. As the gas cools further and contracts further, the volume of the gas will decrease so much that the pressure outside the balloon will cause the flask to suck the balloon in completely.

### Method 3 of 3: Prove Charles's Law Mathematically

#### Step 1. Consider the ideal gas properties that come into play in this process

Jacques Charles proved (and so did Joseph Gay-Lussac later) that the temperature of a gas is directly related to its volume when the pressure and mass of the gas are held constant. This means that, for a given gas, the volume of the gas divided by the temperature of that gas results in the same number for any combination of volume and temperature.

#### Step 2. Make sure you are using the correct units

The volume should be measured in liters. Temperature must be measured in Kelvin. If the values are in different units, use the dimensional analysis properties to convert them to the corresponding units before continuing. Otherwise, your calculations will be incorrect.

#### Step 3. Use the constant k to construct the equation

The initial volume of the gas (V1) divided by the initial gas temperature (T1) is equal to a constant, k. If the volume or temperature of that gas changes, both values will change so that the new volume (V2) divided by the new temperature (V2) will remain equal to the same constant k. What V1/ T1= k and V2/ T2= k, then V1/ T1= V2/ T2.

#### Step 4. Solve the equation to find the unknown variable

When they give you a problem to solve, they will provide you with some of the measurements and ask you to calculate the unknown variable from the equation. Examine the problem to see what the given values are and plug them into the corresponding part of the equation. Once you have all the known values in the equation, simply rearrange it to leave the unknown variable alone and then solve it by applying arithmetic operations. That way, you will have used Charles's law to solve the problem.