# 3.3.2 Pressure & Volume

### Pressure Changes in a Gas

• If the temperature of a gas remains constant, the pressure of the gas changes when it is:
• Compressed – decreases the volume which increases the pressure
• Expanded – increases the volume which decreases the pressure Pressure increases when a gas is compressed

• The pressure produces a net force at right angles to the wall of the gas container (or any surface) Gas molecules bouncing off the walls of a container

• Therefore, if the gas is compressed, the molecules will hit the walls of the container more frequently
• This creates a larger overall net force on the walls which increases the pressure

### Volume & Temperature

• In a gas, the molecles are widely spread
• This makes the gas easy to expand and compress
• Changing the pressure acting on the gas will compress it or allow it to expand if the temperature is kept constant
• When a gas is compressed, the volume is decreased
• The density of the gas increases, allowing more frequent collisions of the molecules on the container wall
• This increases the pressure ### Calculating Change in Pressure & Volume

• For a fixed mass of a gas held at a constant temperature:

pV = constant

• Where:
• p = pressure in pascals (Pa)
• V = volume in metres cubed (m3)
• This means that the pressure and volume are inversely proportional to each other
• When the volume decreases (compression), the pressure increases
• When the volume increases (expansion), the pressure decreases
• This is because when the volume decreases, the same number of particles collide with the walls of a container but more frequently as there is less space
• However, the particles still collide with the same amount of force meaning greater force per unit area (pressure)
• The key assumption is that the temperature and the mass (and number) of the particles remains the same
• This equation can also be rewritten for comparing the pressure and volume before and after a change in a gas:

P1V1 = P2V2

• Where:
• P1 = initial pressure in pascals (Pa)
• V1 = initial volume in metres cubed (m3)
• P2 = final pressure in pascals (Pa)
• V2 = final volume in metres cubed (m3)
• This equation is sometimes referred to as Boyle’s Law Initial pressure and volume, P1 and V1, and final pressure and volume, P2 and V2

#### Worked Example

A gas occupies a volume of 0.70 m³ at a pressure of 200 Pa. Calculate the pressure exerted by the gas if it is compressed to a volume of 0.15 m³.

Assume that the temperature and mass of the gas stay the same. #### Exam Tip

Always check whether your final answer makes sense. If the gas has been compressed, the final pressure is expected to be more than the initial pressure (like in the worked example).

If this is not the case, double-check the rearranging of any formulae and the values put into your calculator. ### Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.
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