CHAPTER 4 THE SECOND LAW
4.3 CONCEPTSDEVELOPED WITHCARNOTENGINES 105
bbbbbb234567890:5 1:0 1:5 2 :0 2 :5
V=m^3p=PaAB^0BC C
0DFigure 4.3 Indicator diagram for a Carnot engine using an ideal gas as the working
substance. In this example,Th D 400 K,TcD 300 K,D1=4,CV;mD.3=2/R,
nD2:41mmol. The processes of paths A!B and C!D are isothermal; those of
paths B!C, B^0 !C^0 , and D!A are adiabatic. The cycle A!B!C!D!A has net
workwD 1:0J; the cycle A!B^0 !C^0 !D!A has net workwD 0:5J.and properties of the state function called entropy. Section4.5uses irreversible processes
to complete the derivation of the mathematical statements given in the box on page 102 ,
Sec.4.6describes some applications, and Sec.4.7is a summary. Finally, Sec.4.8briefly
describes a microscopic, statistical interpretation of entropy.
Carnot engines and Carnot cycles are admittedly outside the normal experience of
chemists, and using them to derive the mathematical statement of the second law may
seem arcane. G. N. Lewis and M. Randall, in their classic 1923 bookThermodynam-
ics and the Free Energy of Chemical Substances,^5 complained of the presentation of
“ ‘cyclical processes’ limping about eccentric and not quite completed cycles.” There
seems, however, to be no way to carry out a rigorousgeneralderivation without in-
voking thermodynamic cycles. You may avoid the details by skipping Secs.4.3–4.5.
(Incidently, the cycles described in these sections are complete!)4.3 Concepts Developed with Carnot Engines
4.3.1 Carnot engines and Carnot cycles
A heat engine, as mentioned in Sec.4.2, is a closed system that converts heat to work
and operates in a cycle. ACarnot engineis a particular kind of heat engine, one that
performsCarnot cycleswith a working substance. A Carnot cycle has four reversible
steps, alternating isothermal and adiabatic; see the examples in Figs.4.3and4.4in which
the working substances are an ideal gas and H 2 O, respectively.
(^5) Ref. [ 104 ], p. 2.