Gas Pressure and Boyle's Law
This topic explains how macroscopic gas properties like pressure and temperature are direct results of the microscopic behaviour of countless moving particles. You will apply this model to calculate how the pressure of a gas changes when its volume is altered at a constant temperature.
Part of the ESAT Physics syllabus — revision for the Engineering and Science Admissions Test (ESAT), the UAT-UK admissions test for Cambridge, Imperial, Oxford and UCL.
Key points
- Gas pressure is the result of the cumulative force from countless gas particles colliding with the walls of their container.
- The temperature of a gas is a measure of the average kinetic energy of its particles. Higher temperature means the particles move, on average, faster.
- Increasing the temperature of a gas in a fixed volume increases its pressure, because the faster particles hit the walls more often and more forcefully.
- At a constant temperature, compressing a gas into a smaller volume increases its pressure because the particles are more crowded and hit the walls more frequently.
- For a fixed mass of gas at constant temperature, pressure is inversely proportional to volume. If you halve the volume, you double the pressure.
Diagram
› Why does this happen?
Why Shrinking a Gas Increases its Pressure (Boyle's Law)
Imagine a fixed number of gas particles in a container. If the temperature is constant, their average speed stays the same. When you decrease the container's volume, you are crowding the same number of particles into a smaller space. This means they have less distance to travel before hitting a wall. As a result, they collide with the walls more frequently. Pressure is caused by the force from these collisions on the container walls. More frequent collisions mean a greater average force on the walls, which results in a higher pressure. This is why halving the volume doubles the pressure.
Why Heating a Gas Increases its Pressure
Temperature is a measure of the average kinetic energy of the gas particles. When you heat a gas, you give its particles more kinetic energy, making them move faster. These faster-moving particles affect the pressure in two ways: 1. They hit the container walls harder, exerting a greater force with each collision. 2. They travel across the container more quickly, so they hit the walls more often. The combination of more frequent and more forceful collisions increases the total force on the walls, raising the pressure.
Formulae
P1 V1 = P2 V2 Use this relationship, known as Boyle's Law, to calculate the new pressure (P2) or volume (V2) of a fixed mass of gas after a change, ONLY when the temperature is held constant.
Definitions
- Pressure (in gases)
- The force exerted per unit area on the surface of a container, caused by the constant, random collisions of gas particles with the container walls.
- Temperature (in gases)
- A macroscopic property that reflects the average kinetic energy of the gas particles. It is not a property of a single particle, but of the gas as a whole.
- Ideal Gas
- A theoretical model of a gas where particles have negligible volume and do not exert forces on each other except during collisions. It's a good approximation for many real gases under normal conditions.
Worked example
A sealed container holds a gas at a pressure of 300 kPa and has a volume of 80 cm3. A piston is slowly pulled outwards, increasing the volume to 240 cm3. Assuming the temperature does not change, what is the new pressure of the gas?
- 1
Identify that the mass of gas and the temperature are constant, so Boyle's Law (P1 × V1 = P2 × V2) applies.
- 2
List the initial and final conditions:
P1 = 300 kPa, V1 = 80 cm3, V2 = 240 cm3 - 3
Rearrange the formula to solve for the final pressure, P2:
P2 = (P1 × V1) / V2 - 4
Substitute the values into the rearranged formula:
P2 = (300 × 80) / 240 - 5
Simplify the calculation.
Notice that 240 is 3 times 80.
So, P2 = 300 / 3 - 6
Calculate the final answer:
P2 = 100 kPa
Answer: 100 kPa
Common mistakes
- ×Applying the P1*V1 = P2*V2 formula when the temperature is not constant. This is the most frequent error. The formula is only valid under isothermal (constant temperature) conditions.
- ×Incorrectly assuming a direct relationship, e.g., thinking that increasing volume increases pressure. Remember it's an inverse relationship: bigger volume means lower pressure.
- ×Making arithmetic mistakes during calculation. A common slip is misplacing a decimal point or mixing up units when a question uses both Pa and kPa.
No-calculator tips
- ✓Think in ratios instead of just plugging in numbers. In the worked example, the volume triples (from 80 to 240 cm3). Since pressure is inversely proportional, the pressure must become one-third of its original value (300 / 3 = 100 kPa).
- ✓Before multiplying large numbers, always look for opportunities to simplify the fraction. For example, in (300 × 80) / 240, you can cancel 80 from the top and bottom, leaving 300 / 3.