entropy change is positive when a gas expands into a larger volume in an
isolated system or when two different gases mix in an isolated system.
Furthermore, the entropy change is positive when heat flows from a hot
body to a cold body (where the two are in contact and together form an
isolated system), and ΔS = 0 when the two bodies reach the same temperature (thermal equilibration). In other words, the entropy change
is always positive for spontaneous (irreversible) processes, and is zero
when the system reaches equilibrium. The entropy change is negative for
nonspontaneous processes. We can summarize these facts as
ΔS > 0 Spontaneous process
ΔS = 0 Reversible process
ΔS < 0 Nonspontaneous process
If we consider the universe as an isolated system, then any natural irreversible process will tend to an increase in entropy. One common
statement of the second law of thermodynamics is that the energy of the
universe is constant but the entropy is tending to a maximum. A more
formal assertion of the second law states that for any change in the
thermodynamic state of a system, the entropy change of the system is
ΔS =
q
T
for a reversible process
ΔS >
q
T
for an irreversible process
2.4.2 The statistical interpretation of entropy
Equation 2.33 tells us that an expansion of a gas will always have a positive
entropy change. From quantum theory and statistical mechanics we
know that a particle has access to more quantized translational energy
states when it occupies a larger volume. We discuss this in more detail in
Chapter 4, and the result tells us that a molecule is able to “spread” its
energy over a larger volume. Entropy can be interpreted as this spreading
of energy. In fact any increase in the degrees of freedom of a molecule or
material corresponds to a higher entropy state. For example, H 2 O has
more ways of vibrating than H 2 and so has more vibrational entropy.
As a simple example illustrating the increase in entropy with volume,
consider a thin nanofilm on a surface (Figure 2.11a). On top of the thin film
we have a layer of firmly attached ions. In the bulk solution we have a large
THE ENTROPY STATE FUNCTION: THE SECOND AND THIRD LAWS
41
isolated system or when two different gases mix in an isolated system.
Furthermore, the entropy change is positive when heat flows from a hot
body to a cold body (where the two are in contact and together form an
isolated system), and ΔS = 0 when the two bodies reach the same temperature (thermal equilibration). In other words, the entropy change
is always positive for spontaneous (irreversible) processes, and is zero
when the system reaches equilibrium. The entropy change is negative for
nonspontaneous processes. We can summarize these facts as
ΔS > 0 Spontaneous process
ΔS = 0 Reversible process
ΔS < 0 Nonspontaneous process
If we consider the universe as an isolated system, then any natural irreversible process will tend to an increase in entropy. One common
statement of the second law of thermodynamics is that the energy of the
universe is constant but the entropy is tending to a maximum. A more
formal assertion of the second law states that for any change in the
thermodynamic state of a system, the entropy change of the system is
ΔS =
q
T
for a reversible process
ΔS >
q
T
for an irreversible process
2.4.2 The statistical interpretation of entropy
Equation 2.33 tells us that an expansion of a gas will always have a positive
entropy change. From quantum theory and statistical mechanics we
know that a particle has access to more quantized translational energy
states when it occupies a larger volume. We discuss this in more detail in
Chapter 4, and the result tells us that a molecule is able to “spread” its
energy over a larger volume. Entropy can be interpreted as this spreading
of energy. In fact any increase in the degrees of freedom of a molecule or
material corresponds to a higher entropy state. For example, H 2 O has
more ways of vibrating than H 2 and so has more vibrational entropy.
As a simple example illustrating the increase in entropy with volume,
consider a thin nanofilm on a surface (Figure 2.11a). On top of the thin film
we have a layer of firmly attached ions. In the bulk solution we have a large
THE ENTROPY STATE FUNCTION: THE SECOND AND THIRD LAWS
41