C
H
A
P
T
E
R
2
0
Entropy and the Second Law
of Thermodynamics
583 583
20-1 ENTROPY
After reading this module, you should be able to . . .
20.01 Identify the second law of thermodynamics: If a
process occurs in a closed system, the entropy of the
system increases for irreversible processes and remains
constant for reversible processes; it never decreases.
20.02 Identify that entropy is a state function (the value for a
particular state of the system does not depend on how
that state is reached).
20.03 Calculate the change in entropy for a process by
integrating the inverse of the temperature (in kelvins) with
respect to the heat Q transferred during the process.
20.04 For a phase change with a constant temperature
process, apply the relationship between the entropy
change ⌬S, the total transferred heat Q, and the temperature T (in kelvins).
20.05 For a temperature change ⌬T that is small relative to
the temperature T, apply the relationship between the
entropy change ⌬S, the transferred heat Q, and the
average temperature T avg (in kelvins).
20.06 For an ideal gas, apply the relationship between the
entropy change ⌬S and the initial and final values of the
pressure and volume.
20.07 Identify that if a process is an irreversible one, the
integration for the entropy change must be done for a
reversible process that takes the system between the
same initial and final states as the irreversible process.
20.08 For stretched rubber, relate the elastic force to the rate
at which the rubber’s entropy changes with the change in
the stretching distance.
● An irreversible process is one that cannot be reversed by
means of small changes in the environment. The direction in
which an irreversible process proceeds is set by the change
in entropy ⌬S of the system undergoing the process. Entropy
S is a state property (or state function) of the system; that is, it
depends only on the state of the system and not on the way in
which the system reached that state. The entropy postulate
states (in part): If an irreversible process occurs in a closed
system, the entropy of the system always increases.
● The entropy change ⌬S for an irreversible process that
takes a system from an initial state i to a final state f is exactly
equal to the entropy change ⌬S for any reversible process
that takes the system between those same two states. We
can compute the latter (but not the former) with
Here Q is the energy transferred as heat to or from the
system during the process, and T is the temperature of the
system in kelvins during the process.
● For a reversible isothermal process, the expression for an
entropy change reduces to
⌬S ϭ S f Ϫ S i ϭ ͵
f
i
dQ
T
.
● When the temperature change
of a system is small relative to the temperature (in kelvins) before and after the process,
the entropy change can be approximated as
where T avg is the system’s average temperature during the
process.
● When an ideal gas changes reversibly from an initial state with
temperature T i and volume V i to a final state with temperature
T f and volume V f , the change ⌬S in the entropy of the gas is
● The second law of thermodynamics, which is an extension
of the entropy postulate, states: If a process occurs in a
closed system, the entropy of the system increases for
irreversible processes and remains constant for reversible
processes. It never decreases. In equation form,
⌬S Ն 0.
⌬S ϭ S f Ϫ S i ϭ nR ln
V f
V i
ϩ nC V ln
T f
T i
.
⌬S ϭ S f Ϫ S i Ϸ
Q
T avg
,
⌬T
⌬S ϭ S f Ϫ S i ϭ
Q
T
.
Learning Objectives
Key Ideas
H
A
P
T
E
R
2
0
Entropy and the Second Law
of Thermodynamics
583 583
20-1 ENTROPY
After reading this module, you should be able to . . .
20.01 Identify the second law of thermodynamics: If a
process occurs in a closed system, the entropy of the
system increases for irreversible processes and remains
constant for reversible processes; it never decreases.
20.02 Identify that entropy is a state function (the value for a
particular state of the system does not depend on how
that state is reached).
20.03 Calculate the change in entropy for a process by
integrating the inverse of the temperature (in kelvins) with
respect to the heat Q transferred during the process.
20.04 For a phase change with a constant temperature
process, apply the relationship between the entropy
change ⌬S, the total transferred heat Q, and the temperature T (in kelvins).
20.05 For a temperature change ⌬T that is small relative to
the temperature T, apply the relationship between the
entropy change ⌬S, the transferred heat Q, and the
average temperature T avg (in kelvins).
20.06 For an ideal gas, apply the relationship between the
entropy change ⌬S and the initial and final values of the
pressure and volume.
20.07 Identify that if a process is an irreversible one, the
integration for the entropy change must be done for a
reversible process that takes the system between the
same initial and final states as the irreversible process.
20.08 For stretched rubber, relate the elastic force to the rate
at which the rubber’s entropy changes with the change in
the stretching distance.
● An irreversible process is one that cannot be reversed by
means of small changes in the environment. The direction in
which an irreversible process proceeds is set by the change
in entropy ⌬S of the system undergoing the process. Entropy
S is a state property (or state function) of the system; that is, it
depends only on the state of the system and not on the way in
which the system reached that state. The entropy postulate
states (in part): If an irreversible process occurs in a closed
system, the entropy of the system always increases.
● The entropy change ⌬S for an irreversible process that
takes a system from an initial state i to a final state f is exactly
equal to the entropy change ⌬S for any reversible process
that takes the system between those same two states. We
can compute the latter (but not the former) with
Here Q is the energy transferred as heat to or from the
system during the process, and T is the temperature of the
system in kelvins during the process.
● For a reversible isothermal process, the expression for an
entropy change reduces to
⌬S ϭ S f Ϫ S i ϭ ͵
f
i
dQ
T
.
● When the temperature change
of a system is small relative to the temperature (in kelvins) before and after the process,
the entropy change can be approximated as
where T avg is the system’s average temperature during the
process.
● When an ideal gas changes reversibly from an initial state with
temperature T i and volume V i to a final state with temperature
T f and volume V f , the change ⌬S in the entropy of the gas is
● The second law of thermodynamics, which is an extension
of the entropy postulate, states: If a process occurs in a
closed system, the entropy of the system increases for
irreversible processes and remains constant for reversible
processes. It never decreases. In equation form,
⌬S Ն 0.
⌬S ϭ S f Ϫ S i ϭ nR ln
V f
V i
ϩ nC V ln
T f
T i
.
⌬S ϭ S f Ϫ S i Ϸ
Q
T avg
,
⌬T
⌬S ϭ S f Ϫ S i ϭ
Q
T
.
Learning Objectives
Key Ideas