16.3 The Second and Third Laws of Thermodynamics

The Second Law of Thermodynamics

In the quest to identify a property that may reliably predict the spontaneity of a process, a promising candidate has been identified: entropy. Processes that involve an increase in entropy of the system (ΔS > 0) are very often spontaneous; however, examples to the contrary are plentiful. By expanding consideration of entropy changes to include the surroundings, we may reach a significant conclusion regarding the relation between this property and spontaneity. In thermodynamic models, the system and surroundings comprise everything, that is, the universe, and so the following is true:

Δ S_{univ} = Δ S_{sys} + Δ S_{surr}

To illustrate this relation, consider again the process of heat flow between two objects, one identified as the system and the other as the surroundings. There are three possibilities for such a process:

The objects are at different temperatures, and heat flows from the hotter to the cooler object. This is always observed to occur spontaneously. Designating the hotter object as the system and invoking the definition of entropy yields the following:
$Δ S_{sys} = \frac{- q _{rev}}{T _{sys}} and Δ S_{surr} = \frac{q _{rev}}{T _{surr}}$

These results lead to a profound statement regarding the relation between entropy and spontaneity known as the second law of thermodynamics: all spontaneous changes cause an increase in the entropy of the universe. A summary of these three relations is provided in Table 16.1.

Table 16.1

The Second Law of Thermodynamics
ΔS $_{u ni v}$ > 0	spontaneous
ΔS $_{u ni v}$ < 0	nonspontaneous (spontaneous in opposite direction)
ΔS $_{u ni v}$ = 0

For many realistic applications, the surroundings are vast in comparison to the system. In such cases, the heat gained or lost by the surroundings as a result of some process represents a very small, nearly infinitesimal, fraction of its total thermal energy. For example, combustion of a fuel in air involves transfer of heat from a system (the fuel and oxygen molecules undergoing reaction) to surroundings that are infinitely more massive (the earth’s atmosphere). As a result, q $_{s u r r}$ is a good approximation of q $_{r e v}$ , and the second law may be stated as the following:

Δ S_{univ} = Δ S_{sys} + Δ S_{surr} = Δ S_{sys} + \frac{q _{surr}}{T}

We may use this equation to predict the spontaneity of a process as illustrated in Example 16.4.

The Third Law of Thermodynamics

The previous section described the various contributions of matter and energy dispersal that contribute to the entropy of a system. With these contributions in mind, consider the entropy of a pure, perfectly crystalline solid possessing no kinetic energy (that is, at a temperature of absolute zero, 0 K). This system may be described by a single microstate, as its purity, perfect crystallinity and complete lack of motion means there is but one possible location for each identical atom or molecule comprising the crystal (W = 1). According to the Boltzmann equation, the entropy of this system is zero.

S = k ln W = k ln (1) = 0

This limiting condition for a system’s entropy represents the third law of thermodynamics: the entropy of a pure, perfect crystalline substance at 0 K is zero.

Careful calorimetric measurements can be made to determine the temperature dependence of a substance’s entropy and to derive absolute entropy values under specific conditions. Standard entropies (S°) are for one mole of substance under standard conditions (a pressure of 1 bar and a temperature of 298.15 K; see details regarding standard conditions in the thermochemistry chapter of this text). The standard entropy change (ΔS°) for a reaction may be computed using standard entropies as shown below:

Δ S ° = \sum ν S ° (products) - \sum ν S ° (reactants)

where ν represents stoichiometric coefficients in the balanced equation representing the process. For example, ΔS° for the following reaction at room temperature

m A + n B ⟶ x C + y D,

is computed as:

= [x S^{\circ} (C) + y S ° (D)] - [m S ° (A) + n S ° (B)]

A partial listing of standard entropies is provided in Table 16.2, and additional values are provided in Appendix G. The example exercises that follow demonstrate the use of S° values in calculating standard entropy changes for physical and chemical processes.

Table 16.2Standard entropies for selected substances measured at 1 atm and 298.15 K. (Values are approximately equal to those measured at 1 bar, the currently accepted standard state pressure.)

Substance	$S °$ (J mol⁻¹ K⁻¹)
carbon
C(s, graphite)	5.740
C(s, diamond)	2.38
CO(g)	197.7
CO₂(g)	213.8
CH₄(g)	186.3
C₂H₄(g)	219.3
C₂H₆(g)	229.2
CH₃OH(l)	126.8
C₂H₅OH(l)

Key Concepts and Summary

The second law of thermodynamics states that a spontaneous process increases the entropy of the universe, S $_{u ni v}$ > 0. If ΔS $_{u ni v}$ < 0, the process is nonspontaneous, and if ΔS $_{u ni v}$ = 0, the system is at equilibrium. The third law of thermodynamics establishes the zero for entropy as that of a perfect, pure crystalline solid at 0 K. With only one possible microstate, the entropy is zero. We may compute the standard entropy change for a process by using standard entropy values for the reactants and products involved in the process.

Key Equations

Δ S ° = \sum ν S ° (products) - \sum ν S ° (reactants)

Δ S = \frac{q _{rev}}{T}