Thermal Physics - Kinetic particle model of matter

The kinetic particle model states that all matter is made of tiny particles in constant, random motion. In solids, particles are closely packed and vibrate about fixed positions. In liquids, particles are close but can slide over each other. In gases, particles are far apart and move at high speeds in all directions.

Brownian motion is the random movement of microscopic particles (like smoke or pollen) suspended in a fluid, caused by collisions with much smaller, fast-moving molecules of the fluid. This provides evidence for the kinetic theory.

Temperature is proportional to the average kinetic energy ($E_k$) of the particles in a substance. As temperature increases, the average speed of the particles increases.

Gas pressure is exerted when gas particles collide with the walls of a container, exerting a force over an area ($P = \frac{F}{A}$). An increase in temperature at constant volume increases the pressure because particles hit the walls more frequently and with greater force.

Boyle's Law states that for a fixed mass of gas at a constant temperature, the pressure $P$ is inversely proportional to the volume $V$. This is represented as $P \propto \frac{1}{V}$ or $PV = \text{constant}$.

Specific Heat Capacity ($c$) is the energy required to raise the temperature of $1\text{ kg}$ of a substance by $1\text{ }^\circ\text{C}$ (or $1\text{ K}$).

Latent Heat ($L$) is the energy required to change the state of $1\text{ kg}$ of a substance without a change in temperature. Specific latent heat of fusion ($L_f$) applies to melting/freezing, while specific latent heat of vaporization ($L_v$) applies to boiling/condensing.

Evaporation is a surface phenomenon where the most energetic particles escape the liquid's surface, lowering the average kinetic energy of the remaining particles and resulting in a cooling effect.