Boyle's law
Thermal Physics - OCR A-Level Physics
Key Definition
Boyle's law
At constant temperature, the pressure of a fixed mass of gas is inversely proportional to its volume: $p \propto 1/V$.
At constant temperature, the pressure of a fixed mass of gas is inversely proportional to its volume: $p \propto 1/V$.
Key Definition
Charles's law
At constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature: $V \propto T$.
At constant pressure, the volume of a fixed mass of gas is directly proportional to its absolute temperature: $V \propto T$.
Key Definition
Pressure law
At constant volume, the pressure of a fixed mass of gas is directly proportional to its absolute temperature: $p \propto T$.
At constant volume, the pressure of a fixed mass of gas is directly proportional to its absolute temperature: $p \propto T$.
$$\frac{p}{T} = \text{constant}$$
- All three laws combine into the equation of state: pV = nRTThe ideal gas equation using amount of substance n (mol) and the molar gas constant R = 8.31 J mol⁻¹ K⁻¹. (for n moles) or pV = NkTThe ideal gas equation using number of molecules N and the Boltzmann constant k = 1.38 × 10⁻²³ J K⁻¹. (for N molecules).
- For a fixed amount of gas: $\frac{p_1 V_1}{T_1} = \frac{p_2 V_2}{T_2}$.
- Boyle's lawFor a fixed mass of gas at constant temperature, pressureForce per unit area. Measured in pascals (Pa), where 1 Pa = 1 N m⁻². is inversely proportional to volume. explains why gas pressureForce per unit area. Measured in pascals (Pa), where 1 Pa = 1 N m⁻². increases when you compress a gas at constant temperature: same number of molecules hitting a smaller area.
- Charles's lawFor a fixed mass of gas at constant pressureForce per unit area. Measured in pascals (Pa), where 1 Pa = 1 N m⁻²., volume is directly proportional to absolute temperature. explains why a balloon expands when heated: molecules move faster, push harder on walls, volume must increase to keep pressure constant.
Common Mistake
MEDIUM
Wrong: Using Celsius temperatures in gas law calculations (e.g. $pV/T$ with $T = 25 ^\circ \text{C}$).
Right: Gas law equations ALWAYS require absolute temperature in Kelvin. Convert first: $T(K) = T(^\circ C) + 273.$
Right: Gas law equations ALWAYS require absolute temperature in Kelvin. Convert first: $T(K) = T(^\circ C) + 273.$