Page 99 - Physical Chemistry

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Chapter 3 An alternative statement of the second law is the Clausius statement:
The Second Law of Thermodynamics
It is impossible for a system to undergo a cyclic process whose sole effects are the
flow of heat into the system from a cold reservoir and the flow of an equal amount
of heat out of the system into a hot reservoir.
Proof of the equivalence of the Clausius and Kelvin–Planck statements is given in
Kestin, sec. 9.3.

3.2 HEAT ENGINES

We shall use the second law to deduce theorems about the efficiency of heat engines.
Chemists have little interest in heat engines, but our study of them is part of a chain
of reasoning that will lead to the criterion for determining the position of chemical
equilibrium in a system. Moreover, study of the efficiency of heat engines is related to
the basic question of what limitations exist on the conversion of heat to work.

Heat Engines
A heat engine converts some of the random molecular energy of heat flow into macro-
scopic mechanical energy (work). The working substance (for example, steam in a
steam engine) is heated in a cylinder, and its expansion moves a piston, thereby doing
mechanical work. If the engine is to operate continuously, the working substance has
to be cooled back to its original state and the piston has to return to its original posi-
tion before we can heat the working substance again and get another work-producing
expansion. Hence the working substance undergoes a cyclic process. The essentials of
the cycle are the absorption of heat q by the working substance from a hot body (for
H
example, the boiler), the performance of work w by the working substance on the
surroundings, and the emission of heat q by the working substance to a cold body
C
(for example, the condenser), with the working substance returning to its original state
at the end of the cycle. The system is the working substance.
Our convention is that w is work done on the system. Work done by the system is
w. Likewise, q means the heat flowing into the system, and q is the heat that flows
C
from the system to the cold body in one cycle. For a heat engine, q 0, w 0,
H
and q 0, so w 0 and q 0. The quantity w is negative for a heat engine be-
C
C
cause the engine does positive work on its surroundings; q is negative for a heat en-
C
gine because positive heat flows out of the system to the cold body.
Although this discussion is an idealization of how real heat engines work, it con-
tains the essential features of a real heat engine.
The efficiency e of a heat engine is the fraction of energy input that appears as use-
ful energy output, that is, that appears as work. The energy input per cycle is the heat
input q to the engine. (The source of this energy might be the burning of oil or coal
H
to heat the boiler.) We have
work output per cycle w 0w0
e (3.1)
energy input per cycle q H q H
For a cycle of operation, the first law gives U 0 q w q q w, and
C
H
w q q C (3.2)
H
where the quantities in (3.2) are for one cycle. Equation (3.2) can be written as q
H
w ( q ); the energy input per cycle, q , is divided between the work output w
C
H
and the heat q discarded to the cold body. Use of (3.2) in (3.1) gives
C
q q C q C
H
e 1 (3.3)
q H q H