Q.Hot air balloons float in air because of the low density of the air inside the balloon. Explain this with the help of an appropriate gas law.

Charles’s Law: Why a Balloon Shrinks in the Cold

Imagine you blow up a balloon on a hot summer day, tie it, and then take it into an air-conditioned room. You’ll see it visibly deflate — not because air is leaking, but because the air inside has cooled. Now reverse it: take that same balloon from a cold room into the sun, and it puffs up again.

That’s Charles’s Law in action. The gas inside the balloon is the same amount (same number of molecules), and the balloon’s skin is flexible enough that the pressure inside stays roughly equal to the outside air pressure. So what changes? Only the temperature and the volume.

The Intuition

Gas molecules are always moving. When you heat a gas, the molecules move faster and hit the walls of the container harder and more often. If the container can expand (like a balloon or a piston), the walls get pushed outward until the pressure balances again. So higher temperature → larger volume. Cool the gas, the molecules slow down, the walls collapse inward — lower temperature → smaller volume.

The key is that this relationship is directly proportional: double the absolute temperature, and the volume doubles. Halve the temperature, and the volume halves.

The Precise Statement

For a fixed mass of gas at constant pressure:

Where:

• $V$ = volume of the gas
• $T$ = absolute temperature (in Kelvin)

If you have two different states of the same gas (same mass, same pressure), you can write:

This is the working form you’ll use in problems.

A Quick Example

A gas occupies 2.0 L at 300 K. What will its volume be at 450 K, pressure constant?

$V_2 = 2.0 \times \frac{450}{300} = 3.0 \text{ L}$ …