Here’s a explanation of how statistical thermodynamics explains phase transitions:
1. Phase Transitions
A phase transition happens when a substance changes from one state to another, like:
- Solid → Liquid (melting)
- Liquid → Gas (boiling)
- Solid → Gas (sublimation)
During a phase transition, the temperature often stays constant, even though energy is being added or removed.
2. Statistical Thermodynamics Perspective
Statistical thermodynamics explains this by looking at the behavior of individual particles (atoms or molecules) and their energies:
- Each particle can occupy many energy levels.
- The distribution of particles among these energy levels depends on temperature.
- Phase transitions occur when the energy of the particles becomes sufficient to overcome the interactions holding them in one phase:
- In melting, particles gain enough energy to move freely past each other.
- In boiling, particles gain enough energy to escape into the gas phase.
- Entropy (a measure of disorder) increases during the transition because particles have more freedom in the new phase.
3. Role of Partition Function
- Statistical thermodynamics uses the partition function, which sums over all possible energy states of the system.
- Changes in the partition function reflect changes in thermodynamic quantities (like internal energy, free energy, and entropy).
- At a phase transition, these quantities change sharply, explaining why energy goes into changing the phase rather than increasing temperature.
In short:
Statistical thermodynamics explains phase transitions by tracking the energies and arrangements of individual particles: when particles gain enough energy to overcome their interactions, the substance changes phase, and the associated entropy and energy changes are predicted by statistical distributions.