The gas laws (AQA A-Level Physics): Revision Notes
The gas laws
Gas properties
When studying the behavior of gases, we need to understand three key properties that can be measured and related to each other.
Volume (V) refers to the space taken up by the gas particles within a container. In physics, volume is always measured in metres cubed (m³). This property represents the three-dimensional space available for the gas particles to move around in.
Temperature (T) is a property that relates to the internal energy of a gas. More specifically, temperature equals the average kinetic energy of the gas particles. When we say a gas has a higher temperature, we mean its particles are moving faster on average. Temperature must be measured in Kelvin (K) when working with gas laws. The Kelvin scale is essential because it starts at absolute zero, where particles have minimum kinetic energy.
The Kelvin scale is critical for gas law calculations because it's an absolute temperature scale starting at zero. This ensures that our proportionality relationships work mathematically - you cannot have negative temperatures in Kelvin, which would cause problems with direct proportionality equations.
Pressure (p) arises from collisions between gas particles and the walls of their container. Each collision exerts a tiny force on the container walls. Pressure is defined as force per unit area, which can be written as:
The SI unit for pressure is the pascal (Pa), where 1 pascal equals a pressure of 1 newton per square metre ().
Boyle's law
Boyle's law describes what happens to the pressure of a gas when its volume changes, provided the temperature stays the same.
Boyle's law states: For a fixed mass of gas at constant temperature, the pressure is inversely proportional to the volume.
Mathematically, this relationship is expressed as:
The inverse proportionality means that when volume increases, pressure decreases by the same factor, and when volume decreases, pressure increases correspondingly. For example, if you halve the volume of a gas container, the pressure doubles.
Why does this happen?
Consider the gas particles moving inside the container. When temperature is constant, the particles travel at a fixed average speed. If we increase the container volume, each particle must travel a greater distance between collisions with the walls. This means fewer collisions occur per unit time, resulting in lower pressure.
Conversely, if we decrease the volume, particles hit the walls more frequently because they have less distance to travel between collisions, causing higher pressure.
Graph characteristics: When plotting Boyle's law with pressure on the y-axis and volume on the x-axis, the relationship produces a curve known as a rectangular hyperbola. The curve approaches both axes but never touches them, showing that as volume becomes very large, pressure approaches zero, and as volume approaches zero, pressure becomes extremely large.
Charles' law
Charles' law describes the relationship between the volume and temperature of a gas when pressure remains constant.
Charles' law states: For a fixed mass of gas at constant pressure, the volume is directly proportional to the absolute temperature.
This can be written as:
Direct proportionality means that if you double the temperature (in Kelvin), the volume doubles. If you increase the temperature by 50%, the volume increases by 50%.
The particle explanation:
Pressure depends on both the collision frequency and the force of each collision. When pressure must remain constant but we increase the temperature, the particles move faster. Faster-moving particles would normally create more frequent and harder collisions, which would increase pressure.
To keep the pressure constant, the volume must expand. This expansion increases the distance particles travel between collisions, reducing the collision frequency enough to compensate for the increased particle speed.
A graph of volume against temperature for Charles' law produces a straight line passing through the origin (when temperature is in Kelvin). The linear relationship clearly demonstrates the direct proportionality between these two variables. This straight-line relationship is why Charles' law is often used experimentally to extrapolate to absolute zero temperature.
The pressure law
The pressure law (sometimes called Gay-Lussac's law) describes how pressure changes with temperature when volume is fixed.
The pressure law states: For a fixed mass of gas at constant volume, the pressure is directly proportional to the absolute temperature.
The mathematical expression is:
This means that doubling the absolute temperature doubles the pressure, and halving the temperature halves the pressure.
Understanding the mechanism:
When the container volume is fixed, the particles have a set distance to travel between collisions with the walls. If we increase the temperature, the particles move faster. Since they're moving faster over the same distance, they collide with the walls more frequently.
Additionally, faster-moving particles transfer more momentum during each collision, making each impact harder. Both effects combine to increase the pressure proportionally with temperature.
The graph of pressure against temperature is a straight line through the origin (when using Kelvin). This linear relationship demonstrates the direct proportionality between pressure and absolute temperature at constant volume.
Key Points to Remember:
- All three gas laws apply only to a fixed mass of gas with one variable held constant
- Boyle's law: Pressure and volume are inversely proportional when temperature is constant ()
- Charles' law: Volume and temperature are directly proportional when pressure is constant ()
- The pressure law: Pressure and temperature are directly proportional when volume is constant ()
- Always use Kelvin for temperature, pascals for pressure, and metres cubed for volume in calculations