Il est possible, en prenant certaines précautions, de...

Il est possible, en prenant certaines précautions, de refroidir de l'eau audessous de $0^{\circ} \mathrm{C}$ sans qu'elle se congèle; on dit qu'elle est en surfusion (cela se produit en particulier dans les nuages). Mais une cause minime (une vibration, une particule solide tombant dans cette eau) peut faire cesser brusquement cet état de faux équilibre, et provoquer la solidification spontanée et très rapide de l'eau en glace. Montrez, en calculant la variation d'enthalpie libre qui accompagne la solidification isotherme d'eau refroidie à $-10^{\circ} \mathrm{C}$, que cette transformation est en effet spontanée.

Il est possible, en prenant certaines précautions, de refroidir de l'eau audessous de $0^{\circ} \mathrm{C}$ sans qu'elle se congèle; on dit qu'elle est en surfusion (cela se produit en particulier dans les nuages). Mais une cause minime (une vibration, une particule solide tombant dans cette eau) peut faire cesser brusquement cet état de faux équilibre, et provoquer la solidification spontanée et très rapide de l'eau en glace.
Montrez, en calculant la variation d'enthalpie libre qui accompagne la solidification isotherme d'eau refroidie à $-10^{\circ} \mathrm{C}$, que cette transformation est en effet spontanée.

Key Concepts

Gibbs Free Energy

Gibbs free energy is a thermodynamic potential that combines enthalpy and entropy to determine the spontaneity of a process at constant temperature and pressure. A process is spontaneous if the change in Gibbs free energy (?G) is negative. This concept allows one to predict whether a phase transition or chemical reaction will proceed without external intervention by evaluating the balance between energy and disorder.

Spontaneous Process

A spontaneous process is one that occurs without the need for continuous external energy input because it results in a decrease in the system’s free energy. In the context of phase transitions, if the change in Gibbs free energy is negative, the transformation will naturally occur, reflecting a state of lower energy and higher probability of occurrence under the given conditions.

Isothermal Process

An isothermal process is one that takes place at a constant temperature. In thermodynamic calculations, working under constant temperature simplifies the expression for the Gibbs free energy change, as the temperature term in ?G = ?H - T?S remains unchanged and directly relates the enthalpy and entropy changes of the transformation.

Phase Transition

Phase transitions involve the change of a substance from one state of matter to another, such as from liquid to solid. This process is often characterized by an energy change associated with breaking or forming intermolecular bonds. Evaluating phase transitions through parameters like the latent heat and associated enthalpy and entropy changes allows for the calculation of the overall free energy change.

Latent Heat of Fusion

The latent heat of fusion is the amount of energy released or absorbed during the phase transition from liquid to solid without a temperature change. It is a key parameter in calculating the enthalpy change (?H) during a phase transition, and it plays a significant role in determining the Gibbs free energy change for the process.

Supercooling

Supercooling refers to the state in which a liquid is cooled below its normal freezing point yet remains in the liquid phase. This metastable condition occurs due to the absence of nucleation sites needed to initiate crystallization. Understanding supercooling involves recognizing that while the liquid is in an energetically unstable state, a slight perturbation or introduction of a nucleation site can lead to a rapid, spontaneous phase transition to the solid state.

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