From a statistical mechanics perspective, the state of matter is determined by the competition between the Average Kinetic Energy (disruptive force) and the Intermolecular Forces (cohesive force).
The Fundamental Postulate: The average kinetic energy of a particle is directly proportional to the absolute temperature:
$$\langle E_k \rangle = \frac{3}{2} k_B T$$
| Property | Solid State | Liquid State | Gaseous State |
|---|---|---|---|
| Energy Ratio | $E_k \ll \text{Potential Energy } (U)$ | $E_k \approx U$ | $E_k \gg U$ |
| Molecular Motion | Restricted to vibrations about fixed lattice positions. | Translational, rotational, and vibrational; particles "slide" over one another. | Random, high-speed translational motion in straight lines. |
| Mean Free Path ($\lambda$) | Negligible; particles are in constant contact. | Very small; slightly larger than molecular diameter. | Large; typically many times the molecular diameter. |
| Collision Frequency | High frequency (vibrational), but no change in position. | Frequent collisions maintain a condensed phase. | Infrequent relative to density; collisions are assumed perfectly elastic. |
| Entropy ($S$) | Minimum; highly ordered crystal lattice. | Intermediate; short-range order, long-range disorder. | Maximum; total spatial disorder. |
Thermodynamic Transitions
According to KMT, when we supply heat to a solid, the amplitude of vibrations increases. At the melting point, the kinetic energy becomes sufficient to overcome the lattice energy. In the gaseous state, we assume the intermolecular forces are effectively zero (except during collisions), leading to the Ideal Gas Law behavior.
Advanced Note: In solids, the kinetic energy is primarily vibrational. In gases, for a monoatomic species, it is entirely translational, whereas for polyatomic gases, internal degrees of freedom (rotation/vibration) contribute to the total molar heat capacity.