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.
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.
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.
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.
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?
We can start off by thinking about this problem logically: if the temperature is decreasing, the molecules in the balloon are slowing down and getting closer together. This will cause the balloon to shrink. Now, the temperature is only decreasing from 293 K to 260 K, so the volume will not decrease by much. We can plug the numbers into this equation and find out how much the balloon will shrink.
The starting volume is 1.00 liters, and the starting temperature is 293 K. The final temperature is 260 K. If we solve for V2, we get 0.887 L as a final volume. You can solve for V2 a couple of different ways: I solved by cross-multiplying the 1 and 260 and then dividing by 293. You could also rewrite this equation as an equality:
V1 x T2 = T1 x V2
1 L x 260 K = V2 x 293.
We would just need to solve for V2 then, which will give us 0.887 L.
Practice Question 2
Let's try a trickier example. This time, your temperature will be given in Celsius, and you must first convert it to Kelvins. This technique was covered in a previous lesson. Say you have a 500 mL unopened bag of potato chips at room temperature (20 degrees Celsius). Now, you take this bag of potato chips outside on a hot summer day when the temperature is 38 degrees Celsius. What is the final volume of the bag of potato chips?
As I mentioned, to solve this, you will need to use Kelvin as a temperature unit. So, to convert degrees Celsius to Kelvins, you must add 273. This makes our room temperature 20 + 273 = 293 Kelvins. It makes our outside temperature 38 + 273 = 311 Kelvins.
Now I think we're ready to start using the equation. Our initial volume is 500 mL, and our initial temperature is 293 Kelvins. Our final temperature is 311 Kelvins. Solving for V2 gives us 531 mL. This makes sense because as the gas is warmed up, the particles speed up and get farther apart, which causes the container to expand.
Near the end of the hot air balloon ride, the torch heating the air in the balloon is used less frequently. As the air in the hot air balloon cools, the particles slow down and move closer together. When the particles move closer together, the air becomes more dense, causing the hot air balloon to sink. This is one of several situations where you can see Charles' Law at work. Charles' Law states that the volume of a gas is directly proportional to the temperature of a gas. Often the equation V1 / T1 = V2 / T2 is used to make calculations involving Charles' Law.
Upon completing this lesson, you will be able to:
- Explain the relationship between temperature and volume using Charles' Law
- Write an equation for Charles' Law
- Identify the units used in this equation
- Solve for variables in the Charles' Law equation