Matter

States of matter, the gas law, changes of state and latent heat, density and pressure.

8 min read

In a solid particles vibrate in fixed positions; in a liquid they touch but move past one another; in a gas they are far apart and move freely. Gas pressure comes from particles colliding with the walls; raising the temperature makes them faster.

For a fixed mass of gas at constant temperature, $P V = constant$ : squeeze the volume and the pressure rises in proportion.

Worked example

Gas at $100 kPa$ fills $0.6 m^{3}$ . Compressed to $0.2 m^{3}$ at the same temperature, find the new pressure.

$P_{1} V_{1} = P_{2} V_{2} \Rightarrow 100 \times 0.6 = P_{2} \times 0.2 \Rightarrow P_{2} = 300 kPa .$

At the melting and boiling points, energy goes into breaking bonds rather than raising temperature. This is latent heat: of *fusion* (melting) and of *vaporisation* (boiling). Energy $= m L$ , where $L$ is the specific latent heat.

Density $ρ = \frac{m}{V}$ . Pressure $P = \frac{F}{A}$ ; the same force over a smaller area gives more pressure. In a liquid, hydrostatic pressure increases with depth: $P = h ρ g$ .

Worked example

Find the pressure $20 m$ deep in water ( $ρ = 1000$ , $g = 10$ ).

$P = h ρ g = 20 \times 1000 \times 10 = 200000 Pa .$

Expecting temperature to rise during a change of state (it stays constant).
Forgetting pressure depends on area (a sharp point gives huge pressure).
Using diameter instead of depth in $P = h ρ g$ .

Matter

States of matter & gases

Changes of state & latent heat

Density & pressure

Common mistakes