54
2 Macroscopic Thermodynamics
within the system. An increase of entropy is thus always associated with unavailable
exportable work. We note also that all entropy generated via irreversible steps in the
engine cycle are exported to the low-temperature heat reservoir during the steps
involved in returning the system to its initial state.
We shall define the efficiency η of the heat engine as the ratio of the work
exported from the system to the heat imported from the hot reservoir, namely, as
η ≡
W export
Q import
= η max −
T low ((S) surr
Q import
,
(2.5.8a)
with η max given via Eq. (2.5.6) by
η max = 1 −
T low
T high
,
(2.5.8b)
and referred to as the maximum efficiency of the heat engine. In particular, because
T low ((S) surr represents work that is inaccessible by virtue of irreversible processes
associated with heat transfers between the system/engine and its surroundings, the
maximal work available for export that can be generated by a heat engine thus occurs
for a fully reversible engine, for which ((S) surr = ((S)
(rev)
surr ≡ 0, in which case,
η = η max . Otherwise, η < η max .
A perfect engine, i.e., an engine capable of converting Q import fully into
exportable work would give (from Eq. (2.5.7))
Q import = W
(perf)
export = Q import
1 −
T low
T high
− T low ((S) surr ,
from which we would find that ((S) surr would be given by
((S) surr = −
Q import
T high
< 0 ,
which violates the Second Law of Thermodynamics. This result is the source of the
Kelvin–Planck version of the Second Law, namely, that ‘There is no perfect engine:
hence, it is impossible to construct a cyclic device which has no effect other than
the conversion of heat into an equivalent amount of work’.
2.5.1 The Carnot Engine and Engine Cycle
A Carnot engine [6] is a device that enables a thermodynamic system to exchange
mechanical work with its surroundings and to exchange energy reversibly with two
thermal reservoirs characterized by temperatures T high and T low . The most common
process by which a Carnot engine operates is that devised by Carnot himself,
2 Macroscopic Thermodynamics
within the system. An increase of entropy is thus always associated with unavailable
exportable work. We note also that all entropy generated via irreversible steps in the
engine cycle are exported to the low-temperature heat reservoir during the steps
involved in returning the system to its initial state.
We shall define the efficiency η of the heat engine as the ratio of the work
exported from the system to the heat imported from the hot reservoir, namely, as
η ≡
W export
Q import
= η max −
T low ((S) surr
Q import
,
(2.5.8a)
with η max given via Eq. (2.5.6) by
η max = 1 −
T low
T high
,
(2.5.8b)
and referred to as the maximum efficiency of the heat engine. In particular, because
T low ((S) surr represents work that is inaccessible by virtue of irreversible processes
associated with heat transfers between the system/engine and its surroundings, the
maximal work available for export that can be generated by a heat engine thus occurs
for a fully reversible engine, for which ((S) surr = ((S)
(rev)
surr ≡ 0, in which case,
η = η max . Otherwise, η < η max .
A perfect engine, i.e., an engine capable of converting Q import fully into
exportable work would give (from Eq. (2.5.7))
Q import = W
(perf)
export = Q import
1 −
T low
T high
− T low ((S) surr ,
from which we would find that ((S) surr would be given by
((S) surr = −
Q import
T high
< 0 ,
which violates the Second Law of Thermodynamics. This result is the source of the
Kelvin–Planck version of the Second Law, namely, that ‘There is no perfect engine:
hence, it is impossible to construct a cyclic device which has no effect other than
the conversion of heat into an equivalent amount of work’.
2.5.1 The Carnot Engine and Engine Cycle
A Carnot engine [6] is a device that enables a thermodynamic system to exchange
mechanical work with its surroundings and to exchange energy reversibly with two
thermal reservoirs characterized by temperatures T high and T low . The most common
process by which a Carnot engine operates is that devised by Carnot himself,