Boyle's law states that volume and pressure are inversely proportional at constant moles and temperature. It's named after Robert Boyle and illustrates how the volume of a container is greatly affected by pressure changes. Now, how do we depict this relationship? When we say they're inversely proportional, we can describe it as volume being inversely proportional to pressure, which means that \( V \propto \frac{1}{P} \). This shows our inverse relationship between volume and pressure. Think of it as volume being the numerator and pressure being the denominator. They're on different levels, so they are different from one another. If one goes up, the other one has to go down.

In this example, if we look at two containers with movable pistons, volume represents the space within the container. If we observe the initial state, the volume is high, indicating that the pressure, represented by the downward force on the piston, is low — which is why the piston hasn't slid down lower. Now, let's say that we gather enough force from the pressure to push down on this piston. We can see that the volume now is smaller, which is a direct result of the pressure being higher.

To depict this inverse relationship graphically, you can show a graph where volume decreases over time, and as a result, the pressure increases over time, demonstrating the inverse relationship between the two variables.

To express Boyle's law formula in a processed form, we write it as \( P_1V_1 = P_2V_2 \). This represents not only our adjusted formula but also the Boyle's law formula where \( P_1 \) is the initial pressure, \( V_1 \) is the initial volume, \( P_2 \) is the final pressure, and \( V_2 \) is the final volume. If you're unsure how these formulas derive from the ideal gas laws, I recommend revisiting those sections in our course or instructional videos. Remember, Boyle's law illustrates that pressure and volume are inversely proportional, meaning if one is high, the other would be low.