### GCSE Physics

Energy
Forces
Forces and Motion
Waves in Matter
Electricity
Magnetism and Electromagnetism
Particle Model of Matter
Atomic Structure
Space Physics

# Volume and Pressure in Gases

The pressure of a gas is caused by the collision of its particles with the walls of the container. The pressure produces a force that acts at right angles to the wall of the gas container, or any surface. This force is acting over the area of the container.

If we increase the number of gas particles in the container while keeping the volume the same, the concentration increases.

At a higher concentration, there is less spacing between the gas particles. As the gas particles can collide with each other, they do not have to travel as far to collide with the walls of the container.

There will also be more particles to collide with and apply force to the same area. So, there will be more frequent collisions and therefore greater pressure.

## Volume and Pressure

If we decrease the volume of the gas container but still have the same number of gas particles, then the particles have less space to move. For example, in the diagram below, the piston is pushed downwards.

There are more particles per unit of volume, which is the same as saying there is a high concentration of particles. As there is a shorter distance between each collision, there will be more collisions, which means greater pressure.

There is an inverse relationship between volume and pressure: as volume increases, pressure decreases, and vice versa.

## Calculating pressure and volume

For a fixed mass at a constant temperature:

• p = Pressure in pascals (Pa)
• V = Volume in metres cubed (m³)

This is another way to look at the equation:

The pressure multiplied by the volume at the start is equal to the pressure multiplied by the volume at the end.

Or

P1V1 = P2V2

• P1 and V1 represent the pressure and volume before the change.
• P2 and V2 represent the pressure and volume after the change.

## Flexible containers

So far, we have assumed that the containers have a fixed shape. However, if the container is flexible, then changing the temperature or concentration will change the volume of the container instead of the pressure.

This occurs because an increase in the number of collisions or the force of collisions will expand the container rather than increase the pressure.

• An example of a flexible container is a balloon

Although in reality, it will most likely increase the volume and the pressure. As there is a limit to how far the flexible container can expand.

## Example

A gas occupies a volume of 0.20 m³, at a pressure of 100 Pa. Calculate the pressure exerted by the gas if it is compressed to a volume of 0.10 m³. Assume that the temperature and mass of the gas stay the same.

Step 1: List the known quantities

$P_{1}$ (initial pressure) = 100 Pa

$V_{1}$ (initial volume) = 0.20 m³

$V_{2}$ (new volume) = 0.10 m³

Step 2: Rearrange the equation $P_{1}V_{1}=P_{2}V_{2}$ to find $P_{2}$:

$P_{2}=\frac{P_{1}\times V_{1}}{V_{2}}$

$P_{2}=\frac{100 \times 0.20}{0.10}$

$P_{2}$ (new pressure) = 200 Pa

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