Thermodynamics and Chemistry

CHAPTER 4 THE SECOND LAW

4.3 CONCEPTSDEVELOPED WITHCARNOTENGINES 107

2 :1

2 :2

2 :3

2 :4

0 1 2

V=10^4 m^3

p=10

5 Pa

2 :5

A B

D C

Figure 4.4 Indicator diagram for a Carnot engine using H 2 O as the working sub-

stance. In this example,Th D 400 K,TcD 396 K,D1=100,wD 1:0J. In

state A, the system consists of one mole of H 2 O(l). The processes (all carried out

reversibly) are: A!B, vaporization of2:54mmol H 2 O at 400 K; B!C, adiabatic

expansion, causing vaporization of an additional7:68mmol; C!D, condensation of

2:50mmol at 396 K; D!A, adiabatic compression returning the system to the initial

state.

The steps of a Carnot cycle are as follows. In this description, thesystemis the working
substance.

Path A!B: A quantity of heatqhis transferred reversibly and isothermally from a heat
reservoir (the “hot” reservoir) at temperatureThto the system, also at temperatureTh.
qhis positive because energy is transferred into the system.

Path B!C: The system undergoes a reversible adiabatic change that does work on the
surroundings and reduces the system temperature toTc.

Path C!D: A quantity of heatqcis transferred reversibly and isothermally from the system
to a second heat reservoir (the “cold” reservoir) at temperatureTc.qcis negative.

Path D!A: The system undergoes a reversible adiabatic change in which work is done on
the system, the temperature returns toTh, and the system returns to its initial state to
complete the cycle.
In one cycle, a quantity of heat is transferred from the hot reservoir to the system, a
portion of this energy is transferred as heat to the cold reservoir, and the remainder of the
energy is the negative net workwdone on the surroundings. (It is the heat transfer to
the cold reservoir that keeps the Carnot engine from being an impossible Kelvin–Planck
engine.) Adjustment of the length of path A!B makes the magnitude ofwas large or
small as desired—note the two cycles with different values ofwdescribed in the caption of
Fig.4.3.

The Carnot engine is an idealized heat engine because its paths are reversible pro-

cesses. It does not resemble the design of any practical steam engine. In a typical

working steam engine, such as those once used for motive power in train locomotives

and steamships, the cylinder contains anopensystem that undergoes the following ir-

reversible steps in each cycle: (1) high-pressure steam enters the cylinder from a boiler