6.10 - Pressure & Volume

Pressure and volume are inversely proportional

For a fixed mass of gas kept at a constant temperature, pressure and volume are inversely proportional:

• When volume goes up, pressure goes down.
• When volume goes down, pressure goes up.

Why pressure and volume change together

• Gas pressure comes from gas particles colliding with the walls of their container.
• Reducing the volume squeezes the same particles into a smaller space. They hit the walls more frequently, so pressure increases.
• Increasing the volume spreads the particles out. They hit the walls less frequently, so pressure decreases.
• At constant temperature, the particles keep the same average speed, so only the frequency of collisions changes.

The pressure-volume formula (pV = constant)

For a fixed mass of gas at a constant temperature:

$$pV=\text{constant}$$

This can be written to compare starting and final states:

Where:

• $p_1,p_2$ = Pressure, in pascals (Pa)
• $V_1,V_2$ = Volume, in cubic metres (m³)

Pressure-volume graph

• A graph of pressure against volume is a curve that falls steeply at first and levels off ($p\propto \frac{1}{V}$).
• This formula only holds for a fixed mass of gas at a constant temperature.

Worked example - New pressure with pV = constant

A fixed mass of gas has a volume of 0.50 m³ at a pressure of 200,000 Pa. It's slowly compressed to a volume of 0.20 m³ at constant temperature. Calculate its new pressure.