Entropy and the Second Law of Thermodynamics

When NH₄Cl goes into solution, the NH₄⁺ and Cl^- ions leave the highly ordered environment of the crystal to enter the chaotic world of a solution. This increase in disorder is the driving force for the endothermic dissolution of NH₄Cl.

The state function which measures disorder is the entropy, S, and the second law of thermodynamics may be stated as follows: The entropy of the universe or of an isolated system always increases when a spontaneous irreversible process occurs; entropy remains constant in a reversible process, i.e., a process which remains at equilibrium for every step along the way,

           (1.1)

The distinction between reversible and irreversible processes is illustrated by the following example.

Example

Consider a mixture of liquid and solid benzene at its normal freezing point, 5.45°C. If the temperature is raised by a tiny amount, say to 5.46°C, the solid portion will gradually melt; if the temperature were decreased to 5.44°C, the liquid would gradually crystallize. Freezing and melting are reversible processes at 5.45°C.

It is possible to cool liquid benzene to a temperature below the normal freezing point, say to 2°C, without crystallization. The liquid is then said to be supercooled. If a tiny crystal of solid benzene is added, the liquid will crystallize spontaneously and irreversibly. Raising the temperature to 2.01°C (or even to 3°C) will not stop the crystallization. One would have to raise the temperature to above 5.45°C to restore the liquid state. The crystallization of liquid benzene at 2.00°C is an example of an irreversible process.  For a reversible process, the change in a system's entropy is:

      (1.2)

Since entropy is a state function, we can use a reversible process with the same initial and final states to calculate the entropy change that occurs in an irreversible process.  Eq. (1.2) gives us a criterion for spontaneity, but it is restricted to systems that are not in thermal or mechanical contact with the surroundings. A more useful criterion is based on the Gibbs free energy, G, defined by

  (1.3)

Equation (1.2) leads to the following criterion for spontaneity for a process occurring at constant temperature and pressure, but with the system in thermal and mechanical contact with the surroundings: The Gibbs free energy decreases for a spontaneous (irreversible) process and remains constant for an equilibrium (reversible) process.

    (1.4)

G decreases for a spontaneous process, like the energy of a mechanical system. Since ΔG incorporates both driving forces for spontaneity—enthalpy (energy) decrease and entropy (disorder) increase—an endothermic process may be spontaneous if the increase in disorder is big enough to counteract the unfavorable enthalpy change, and a process that leads to increased order (negative ΔS) may be spontaneous if the process is sufficiently exothermic (negative ΔH).