1.3.9 The Second Law of Thermodynamics
The second law of thermodynamics was formulated following many attempts
undertaken for the efficient conversion of heat into work and, as such, its early
development was very much focused on engineering applications related to heat
engine efficiency. The second law can be stated in many different ways. The KelvinPlanck statement in the context of heat engines can be expressed in the following
manner; “No process is possible whose sole effect is the absorption of heat from a
temperature reservoir and the conversion of this heat completely into work”. The
second law, like the first, is expressed in negative terms like “it is not possible” and,
consequently, the second law places limits on what can be achieved.
When the isothermal expansion of an ideal gas was considered in Sect. 1.3.4 it
was evident that there was no change in the internal energy E of the system. In this
context, one can regard the system as a cylinder fitted with a piston and in contact
with an external reservoir at a constant temperature T as shown in Fig. 1.1.
Since ΔE ¼ 0 for the isothermal process, this implies that Q ¼ W so that all the
heat transfer from the single reservoir has been converted into work and it would
appear that the second law has been violated in this process. Certainly, all the heat
has been converted into work but this is not the “the sole effect” for the process as
specified in the Kelvin-Planck statement of the law: instead, the piston has moved
from some initial position to some final position during the expansion and, accordingly, the absorption of heat and the conversion of this heat completely into work is
not the “sole effect”. It would be necessary for the piston to return to its initial
position following the process of heat transfer and this explains why heat engines
work in a cyclic manner.
A thermodynamic property of a system exists, called the entropy, S, which was
introduced into thermodynamics by Clausius, and an infinitesimal change in this
property is given by
dS ¼
dQ rev
T
,
ð1:37Þ
Q
reservoir T
initial
final
piston
Fig. 1.1 Isothermal
expansion of an ideal gas in
contact with a constant
temperature reservoir
1.3 Some Elements of Thermodynamics
11
The second law of thermodynamics was formulated following many attempts
undertaken for the efficient conversion of heat into work and, as such, its early
development was very much focused on engineering applications related to heat
engine efficiency. The second law can be stated in many different ways. The KelvinPlanck statement in the context of heat engines can be expressed in the following
manner; “No process is possible whose sole effect is the absorption of heat from a
temperature reservoir and the conversion of this heat completely into work”. The
second law, like the first, is expressed in negative terms like “it is not possible” and,
consequently, the second law places limits on what can be achieved.
When the isothermal expansion of an ideal gas was considered in Sect. 1.3.4 it
was evident that there was no change in the internal energy E of the system. In this
context, one can regard the system as a cylinder fitted with a piston and in contact
with an external reservoir at a constant temperature T as shown in Fig. 1.1.
Since ΔE ¼ 0 for the isothermal process, this implies that Q ¼ W so that all the
heat transfer from the single reservoir has been converted into work and it would
appear that the second law has been violated in this process. Certainly, all the heat
has been converted into work but this is not the “the sole effect” for the process as
specified in the Kelvin-Planck statement of the law: instead, the piston has moved
from some initial position to some final position during the expansion and, accordingly, the absorption of heat and the conversion of this heat completely into work is
not the “sole effect”. It would be necessary for the piston to return to its initial
position following the process of heat transfer and this explains why heat engines
work in a cyclic manner.
A thermodynamic property of a system exists, called the entropy, S, which was
introduced into thermodynamics by Clausius, and an infinitesimal change in this
property is given by
dS ¼
dQ rev
T
,
ð1:37Þ
Q
reservoir T
initial
final
piston
Fig. 1.1 Isothermal
expansion of an ideal gas in
contact with a constant
temperature reservoir
1.3 Some Elements of Thermodynamics
11