Particle Motion and Gas Pressure

Blow up a balloon and it pushes back against your fingers; leave a sealed can of fizzy drink in a hot car and it can burst. Both happen because a gas exerts a pressure on the walls of its container — and that pressure comes from countless tiny particles, in constant random motion, drumming against those walls. Heat the gas and the particles move faster, hitting the walls harder and more often, so the pressure climbs. This lesson, part of Topic P1 (Matter) of OCR Gateway Science A, explains gas pressure using the particle model, links temperature to the mean kinetic energy of the particles, introduces the kelvin scale and absolute zero, and (Higher tier) looks at how changing the volume of a gas changes its pressure.

By the end of this lesson you should be able to explain gas pressure using the particle model, relate temperature to the mean kinetic energy of particles, describe the pressure–temperature relationship at constant volume, convert between °C and kelvin, and (Higher tier) explain how changing the volume of a gas affects its pressure.

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How a Gas Exerts Pressure

The particles in a gas are in constant, random motion, moving quickly in all directions. As they move they collide with the walls of their container. Each collision gives the wall a tiny push (a small force). With an enormous number of particles colliding every second, these pushes add up to a steady, outward force on the walls. The pressure of the gas is this force spread over the area of the wall:

$\text{pressure} = \dfrac{\text{force}}{\text{area}}$pressure=areaforce​

So gas pressure is caused by the particles of the gas colliding with the walls of the container. The more frequent and the harder these collisions are, the greater the pressure. This is why a gas pushes outward equally in all directions — its particles are striking every wall from inside.

Exam Tip: The cause of gas pressure is always collisions of the gas particles with the container walls. A complete answer says the particles are in constant random motion and that each collision exerts a force on the wall; many collisions per second produce the pressure.

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Temperature and the Mean Kinetic Energy of Particles

The temperature of a gas is a measure of the mean (average) kinetic energy of its particles. The hotter the gas, the faster its particles move on average, and the more kinetic energy they have. This is the crucial link between what you can measure (temperature) and what the particles are doing (moving):

• higher temperature → particles have more kinetic energy → particles move faster (on average);
• lower temperature → particles have less kinetic energy → particles move more slowly.

This relationship is the key to understanding how a gas behaves when it is heated or cooled, because changing the temperature changes how fast the particles are moving, and that changes how they collide with the walls.

Exam Tip: Temperature is the average kinetic energy of the particles. Note "average" (or "mean") — at any instant some particles move faster and some slower, but the average rises with temperature.

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The Pressure–Temperature Relationship (Constant Volume)

Consider a gas in a sealed, rigid container so its volume cannot change. What happens to the pressure if you heat the gas?

As the temperature rises:

1. the particles gain kinetic energy and move faster;
2. faster particles hit the walls harder (each collision exerts a bigger force) and more often (they reach the walls more frequently);
3. so the total force on the walls increases, and since the area is unchanged, the pressure increases.

So, at constant volume, increasing the temperature of a gas increases its pressure, and cooling it decreases the pressure. This is why an aerosol can carries a warning never to heat it: the gas inside would reach a pressure high enough to burst the can.

Exam Tip: To explain why heating a fixed volume of gas raises its pressure, give the full chain: hotter → particles move faster → hit the walls harder and more often → more force on the walls → higher pressure. Examiners look for both "harder" and "more often".

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Absolute Zero and the Kelvin Scale

If cooling a gas makes its particles move more slowly, what happens if you keep cooling? The particles move slower and slower, with less and less kinetic energy. There is a temperature at which the particles have the least possible kinetic energy and effectively stop moving — this is the coldest possible temperature, called absolute zero. It is about $-273\,°\text{C}$−273°C.

Because absolute zero is a natural "bottom" to temperature, scientists use a scale that starts there: the kelvin scale (unit: kelvin, K). On this scale:

• $0 \text{ K}$0 K is absolute zero ($-273\,°\text{C}$−273°C);
• a change of $1 \text{ K}$1 K is the same size as a change of $1\,°\text{C}$1°C;
• to convert, you simply add or subtract $273$273.

$\text{temperature in K} = \text{temperature in } °\text{C} + 273$temperature in K=temperature in °C+273 $\text{temperature in } °\text{C} = \text{temperature in K} - 273$temperature in °C=temperature in K−273

Temperature in °C	Temperature in K
$-273$−273 (absolute zero)	$0$0
$0$0 (ice melts)	$273$273
$25$25 (room temperature)	$298$298
$100$100 (water boils)	$373$373

Worked Example 1 — Converting °C to kelvin

Convert $27\,°\text{C}$27°C to kelvin.

Step 1 — use the rule: $\text{K} = °\text{C} + 273$K=°C+273.

Step 2 — substitute: $\text{K} = 27 + 273$K=27+273.

Step 3 — calculate: $\text{K} = 300 \text{ K}$K=300 K.

Answer: $27\,°\text{C} = 300 \text{ K}$27°C=300 K.

Worked Example 2 — Converting kelvin to °C

Convert $250 \text{ K}$250 K to degrees Celsius.

Step 1 — use the rule: $°\text{C} = \text{K} - 273$°C=K−273.

Step 2 — substitute: $°\text{C} = 250 - 273$°C=250−273.

Step 3 — calculate: $°\text{C} = -23\,°\text{C}$°C=−23°C.

Answer: $250 \text{ K} = -23\,°\text{C}$250 K=−23°C.

The kelvin scale matters because the kinetic energy of the particles is proportional to the temperature in kelvin. At absolute zero ($0 \text{ K}$0 K) the particles have essentially no kinetic energy; doubling the kelvin temperature roughly doubles the average kinetic energy. (This is why kelvin, not Celsius, is used in gas calculations.)

Worked Example 3 — Why the kelvin scale matters for energy

A gas is heated from $27\,°\text{C}$27°C to $327\,°\text{C}$327°C. Show that the average kinetic energy of its particles roughly doubles, and explain why you must use the kelvin scale to see this.

Step 1 — convert both temperatures to kelvin: $27 + 273 = 300 \text{ K}$27+273=300 K and $327 + 273 = 600 \text{ K}$327+273=600 K.

Step 2 — compare the kelvin temperatures: $600 \text{ K}$600 K is twice $300 \text{ K}$300 K.

Step 3 — apply the proportionality: because the average kinetic energy of the particles is proportional to the temperature in kelvin, doubling the kelvin temperature doubles the average kinetic energy.