Volume and pressure

Gas Pressure and Volume

Imagine pulling back the plunger on a sealed, empty plastic syringe—the further you pull it, the less the air inside pushes back against your hand. According to the kinetic theory of matter, gases consist of constantly moving particles. Gas pressure is the total force exerted by these gas particles colliding at right angles with the walls of their container per unit area.

Temperature is a measure of the average kinetic energy of the gas particles.
If the temperature of a gas remains constant, the average particle velocity (speed) stays exactly the same, regardless of how much space the gas occupies.
Each individual collision with the wall exerts a tiny force.

Why Increasing Volume Decreases Pressure

When a gas expands and its volume increases at a constant temperature, the pressure decreases. This happens through a specific step-by-step mechanism:

The same number of gas particles now occupies a larger space, so the gas becomes less dense and particles are more spread out.
Because the space is larger, the particles must travel a greater distance between the container walls.
Since their average speed has not changed (because temperature is constant), this increased distance results in a lower collision frequency—the particles hit the walls less often per second.
Although each individual impact hits with the same force as before, the reduced number of collisions per second means the total force exerted on the walls decreases.
Since pressure is force per unit area ( $p = \frac{F}{A}$ ), a lower total force spread over a larger surface area results in a lower pressure.

Inverse Proportionality and Boyle's Law

For a fixed mass of gas held at a constant temperature, pressure and volume are inversely proportional. This means that if you double the volume of the gas, the pressure is halved. If you halve the volume, the pressure doubles.

Because they change at the exact same rate in opposite directions, multiplying the pressure by the volume always produces a constant value ( $p \times V = \text{constant}$ ). This relationship is expressed in the equation:

p_1 V_1 = p_2 V_2

Where:

$p_1$ and $p_2$ = initial and final pressures in Pascal (Pa)
$V_1$ and $V_2$ = initial and final volumes in cubic metres ( $m^3$ ) or cubic centimetres ( $cm^3$ )

Worked Example

A sealed weather balloon holds a gas with a volume of $2.5\,m^3$ at a pressure of $150,000\,Pa$ . As it rises slightly, the gas expands to a new volume of $5.0\,m^3$ . Assuming the temperature inside the balloon remains constant, calculate the new pressure of the gas.

Step 1: Identify the known values.

$p_1 = 150,000\,Pa$
$V_1 = 2.5\,m^3$
$V_2 = 5.0\,m^3$

Step 2: Substitute these values into the equation.

$150,000 \times 2.5 = p_2 \times 5.0$

Step 3: Calculate the constant ( $p_1 \times V_1$ ).

$375,000 = p_2 \times 5.0$

Step 4: Rearrange to solve for the final pressure ( $p_2$ ).

$p_2 = \frac{375,000}{5.0}$
$p_2 = 75,000\,Pa$

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Exam Tips

Common Mistake
Students often say that particles 'move slower' when the volume increases to explain the drop in pressure, but remember that particle speed is determined only by temperature.
2
In 4-mark explanation questions, examiners explicitly look for the phrase 'collision frequency' or 'fewer collisions per second'—simply writing 'fewer collisions' is usually not enough to get the mark.
3
Always state that gas particles collide 'at right angles' or 'normal to the surface' when defining gas pressure to secure full marks.
4
Higher tier students: You can also explain this mechanism in terms of momentum; fewer collisions mean a lower rate of change of momentum at the walls, resulting in a lower force.

Key Terms(8)

Kinetic theory of matter: A model stating that all matter is made of particles in constant motion, used to explain the properties of solids, liquids, and gases.
Gas pressure: The total force exerted by gas particles colliding at right angles with the walls of their container per unit area.
Temperature: A measure of the average kinetic energy of the particles in a substance.
Kinetic energy: The energy an object or particle possesses due to its motion.
Particle velocity: The speed and direction of an individual particle's movement.
Collision frequency: The number of collisions between gas particles and the container walls occurring per unit of time (usually per second).
Inversely proportional: A relationship where one variable increases at the same rate the other decreases, such that their product remains constant.
Pascal (Pa): The standard SI unit of pressure, equivalent to one Newton of force per square metre (1 N/m²).

Previous Subtopic: Compression and expansionCompression and expansion Next Subtopic: Work done on a gasWork done on a gas

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Key Terms(8)

Kinetic theory of matter: A model stating that all matter is made of particles in constant motion, used to explain the properties of solids, liquids, and gases.
Gas pressure: The total force exerted by gas particles colliding at right angles with the walls of their container per unit area.
Temperature: A measure of the average kinetic energy of the particles in a substance.
Kinetic energy: The energy an object or particle possesses due to its motion.
Particle velocity: The speed and direction of an individual particle's movement.
Collision frequency: The number of collisions between gas particles and the container walls occurring per unit of time (usually per second).
Inversely proportional: A relationship where one variable increases at the same rate the other decreases, such that their product remains constant.
Pascal (Pa): The standard SI unit of pressure, equivalent to one Newton of force per square metre (1 N/m²).

Volume and pressure

Gas Pressure and Volume

Temperature is a measure of the average kinetic energy of the gas particles.
If the temperature of a gas remains constant, the average particle velocity (speed) stays exactly the same, regardless of how much space the gas occupies.
Each individual collision with the wall exerts a tiny force.

Why Increasing Volume Decreases Pressure

When a gas expands and its volume increases at a constant temperature, the pressure decreases. This happens through a specific step-by-step mechanism:

The same number of gas particles now occupies a larger space, so the gas becomes less dense and particles are more spread out.
Because the space is larger, the particles must travel a greater distance between the container walls.
Since their average speed has not changed (because temperature is constant), this increased distance results in a lower collision frequency—the particles hit the walls less often per second.
Although each individual impact hits with the same force as before, the reduced number of collisions per second means the total force exerted on the walls decreases.
Since pressure is force per unit area ( $p = \frac{F}{A}$ ), a lower total force spread over a larger surface area results in a lower pressure.

Inverse Proportionality and Boyle's Law

p_1 V_1 = p_2 V_2

Where:

$p_1$ and $p_2$ = initial and final pressures in Pascal (Pa)
$V_1$ and $V_2$ = initial and final volumes in cubic metres ( $m^3$ ) or cubic centimetres ( $cm^3$ )

Worked Example

Step 1: Identify the known values.

$p_1 = 150,000\,Pa$
$V_1 = 2.5\,m^3$
$V_2 = 5.0\,m^3$

Step 2: Substitute these values into the equation.

$150,000 \times 2.5 = p_2 \times 5.0$

Step 3: Calculate the constant ( $p_1 \times V_1$ ).

$375,000 = p_2 \times 5.0$

Step 4: Rearrange to solve for the final pressure ( $p_2$ ).

$p_2 = \frac{375,000}{5.0}$
$p_2 = 75,000\,Pa$

Sign up to continue reading

Get full access to revision notes, key terms, and exam tips for every subtopic.

Exam Tips

Common Mistake
Students often say that particles 'move slower' when the volume increases to explain the drop in pressure, but remember that particle speed is determined only by temperature.
2
In 4-mark explanation questions, examiners explicitly look for the phrase 'collision frequency' or 'fewer collisions per second'—simply writing 'fewer collisions' is usually not enough to get the mark.
3
Always state that gas particles collide 'at right angles' or 'normal to the surface' when defining gas pressure to secure full marks.
4
Higher tier students: You can also explain this mechanism in terms of momentum; fewer collisions mean a lower rate of change of momentum at the walls, resulting in a lower force.

Key Terms(8)

Kinetic theory of matter: A model stating that all matter is made of particles in constant motion, used to explain the properties of solids, liquids, and gases.
Gas pressure: The total force exerted by gas particles colliding at right angles with the walls of their container per unit area.
Temperature: A measure of the average kinetic energy of the particles in a substance.
Kinetic energy: The energy an object or particle possesses due to its motion.
Particle velocity: The speed and direction of an individual particle's movement.
Collision frequency: The number of collisions between gas particles and the container walls occurring per unit of time (usually per second).
Inversely proportional: A relationship where one variable increases at the same rate the other decreases, such that their product remains constant.
Pascal (Pa): The standard SI unit of pressure, equivalent to one Newton of force per square metre (1 N/m²).

Previous Subtopic: Compression and expansionCompression and expansion Next Subtopic: Work done on a gasWork done on a gas

Back to Volume and pressure

Put your knowledge into practice — try past paper questions for Physics A

Key Terms(8)

Kinetic theory of matter: A model stating that all matter is made of particles in constant motion, used to explain the properties of solids, liquids, and gases.
Gas pressure: The total force exerted by gas particles colliding at right angles with the walls of their container per unit area.
Temperature: A measure of the average kinetic energy of the particles in a substance.
Kinetic energy: The energy an object or particle possesses due to its motion.
Particle velocity: The speed and direction of an individual particle's movement.
Collision frequency: The number of collisions between gas particles and the container walls occurring per unit of time (usually per second).
Inversely proportional: A relationship where one variable increases at the same rate the other decreases, such that their product remains constant.
Pascal (Pa): The standard SI unit of pressure, equivalent to one Newton of force per square metre (1 N/m²).