Q.(a) A balloon is filled with hydrogen at room temperature. It will burst if pressure exceeds 0.25 bar. If at 1 bar pressure the gas occupies 2.40 L volume, upto what volume can the balloon be expanded? [2]

You are sitting on a bicycle pump. The handle is up, the cylinder is full of air. Now push the handle down. The air inside gets squashed into a smaller space — its volume decreases. At the same time, you feel the resistance building: the air is pushing back harder. That is pressure increasing.

That is the raw physical feeling of Boyle's Law. Squeeze a gas, it fights back more. Let it expand, it relaxes.

Now the precise idea: if you take a fixed amount of gas (no air leaking in or out) and keep its temperature absolutely constant, then the volume it occupies and the pressure it exerts are inversely proportional. Double the pressure, the volume halves. Triple the pressure, the volume shrinks to one-third. Halve the pressure, the volume doubles.

Mathematically, this is written as:

Or, more usefully, as a product that stays constant:

where $k$ is some constant number for that particular sample of gas at that temperature.

Why does this happen? Imagine the gas as billions of tiny balls (molecules) zipping around in a box. Pressure comes from them banging into the walls. If you shrink the box, each molecule has less distance to travel between walls, so it hits the walls more often. More collisions per second means higher pressure. The molecules themselves haven't changed speed (temperature is constant), but they are now crowded into a smaller space, so the wall gets hit more frequently. …