7. Gas Laws

The behaviour of gases under changing conditions of pressure, volume, and temperature is described by a set of empirical laws, collectively known as the gas laws, which apply closely to an idealised gas (a hypothetical gas that perfectly obeys these relationships) and reasonably well to most real gases under ordinary conditions of moderate pressure and temperature.

7.1 Boyle's Law

Formulated by Robert Boyle in 1662, this law states that at constant temperature, the volume (V) of a fixed mass of gas is inversely proportional to its pressure (P). In other words, if temperature is held constant, compressing a gas into a smaller volume increases its pressure proportionally, and vice versa. Mathematically: P ∝ 1/V at constant T, or equivalently P₁V₁ = P₂V₂ for a fixed mass of gas at constant temperature. This is why, for example, a sealed bag of chips appears to puff up (its internal air expands) when carried up to a high altitude where atmospheric (external) pressure is lower, and why a bicycle pump gets progressively harder to push as the air inside is compressed to a smaller volume at higher pressure.

7.2 Charles's Law

Formulated by Jacques Charles, this law states that at constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature (measured in kelvin). Mathematically: V ∝ T at constant P, or V₁/T₁ = V₂/T₂. This law also implies that the volume of a gas decreases linearly as its temperature is reduced, and if extrapolated, would theoretically reach zero volume at absolute zero (0 K) — this extrapolation is, in fact, one of the ways absolute zero was originally deduced. A hot air balloon rises because the air inside it is heated, causing it to expand (by Charles's law) and become less dense than the surrounding cooler air, generating buoyant lift.

7.3 Gay-Lussac's Law (Pressure Law)

This law, attributed to Joseph Gay-Lussac (and sometimes credited earlier to Guillaume Amontons), states that at constant volume, the pressure of a fixed mass of gas is directly proportional to its absolute temperature. Mathematically: P ∝ T at constant V, or P₁/T₁ = P₂/T₂. This explains why aerosol spray cans, LPG cylinders, and car tyres carry warnings against exposure to high heat or fire — heating a gas held at essentially constant volume inside a rigid, sealed container causes its pressure to rise sharply, which can lead to a dangerous explosion if the pressure exceeds the container's strength.

7.4 The Combined Gas Law and the Ideal Gas Equation

Combining Boyle's law, Charles's law, and Gay-Lussac's law gives the combined gas law, which relates pressure, volume, and temperature together for a fixed mass of gas: (P₁V₁)/T₁ = (P₂V₂)/T₂. Extending this relationship to relate these quantities to the actual amount of gas present (measured in moles, n) gives the ideal gas equation (also called the equation of state of an ideal gas): PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, T is the absolute temperature in kelvin, and R is the universal (molar) gas constant, whose value is approximately 8.314 J/(mol·K) (equivalently about 0.0821 L·atm/(mol·K)). This single equation summarises the macroscopic behaviour of an ideal gas and reduces to each of Boyle's, Charles's, and Gay-Lussac's laws individually when the other appropriate variable(s) are held constant.

7.5 Quick Reference: The Gas Laws