Very good question; the answer explains how a hot air balloon works!

First, we start by saying that hot air, or air with a higher temperature, is less dense than cold air. What this means is that for a little space, a lot more cold air particles can fit in the space than hot air particles will fit.

Why is this?

Let’s think about a box with a lot of hot air particles in it. When the air is hot, the air particles have more velocity, and this means the air particles hit each other and get knocked around. This knocking around makes the air particles want to spread out from each other, because when each particle gets hit, it wants to fly to an area where it won’t get hit. If the box has a lot of cold air particles, then the articles don’t move around so much, and don’t mind getting hit by each other. The result is that you can fit much more cold air particles into a box than you can fit hot air particles. When you count the mass of each particle, this will tell you thata box filled with hot air will weigh much less than the same box filled with cold air. This is how we can think of density; it is how much mass you can fit into an amount of space, where right now our space is a box.

Now if we take this example of a box, and apply it to a ballon, we can figure out why hot stuff rises. Stuff that is really dense likes to sink to the bottom, while a material that is not so dense will want to float to the top. This is why a ship will always float on the sea, since the ship is much less dense than water. Even though the ship may be really big, its mass is still more spread out amongst the ship, since its density is small. Water, on the other hand, is pretty heavy for a given amount of space, and very stuffed into a small space, meaning it will sink to the bottom.

This is the same with hot and cold air. The dense, cold air will sink to the bottom, while a balloon filled with hot air will rise to the top. Note that we don’t care about how big the balloon is, and only care about how hot it is. I hope this answers your question!