Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

Weights and Measures held in 1954, the triple point of water (the state at
which all three phases of water exist in equilibrium) was assigned the value
273.16 K (Fig. 6–45). The magnitude of a kelvinis defined as 1/273.16 of
the temperature interval between absolute zero and the triple-point tempera-
ture of water. The magnitudes of temperature units on the Kelvin and
Celsius scales are identical (1 K
1°C). The temperatures on these two
scales differ by a constant 273.15:

(6–17)

Even though the thermodynamic temperature scale is defined with the help
of the reversible heat engines, it is not possible, nor is it practical, to actually
operate such an engine to determine numerical values on the absolute tempera-
ture scale. Absolute temperatures can be measured accurately by other means,
such as the constant-volume ideal-gas thermometer together with extrapola-
tion techniques as discussed in Chap. 1. The validity of Eq. 6–16 can be
demonstrated from physical considerations for a reversible cycle using an
ideal gas as the working fluid.

6–10 ■ THE CARNOT HEAT ENGINE

The hypothetical heat engine that operates on the reversible Carnot cycle is
called the Carnot heat engine.The thermal efficiency of any heat engine,
reversible or irreversible, is given by Eq. 6–6 as

where QHis heat transferred to the heat engine from a high-temperature
reservoir at TH, and QLis heat rejected to a low-temperature reservoir at TL.
For reversible heat engines, the heat transfer ratio in the above relation can
be replaced by the ratio of the absolute temperatures of the two reservoirs,
as given by Eq. 6–16. Then the efficiency of a Carnot engine, or any
reversible heat engine, becomes

(6–18)

This relation is often referred to as the Carnot efficiency, since the
Carnot heat engine is the best known reversible engine. This is the highest
efficiency a heat engine operating between the two thermal energy reser-
voirs at temperatures TLand THcan have(Fig. 6–46). All irreversible (i.e.,
actual) heat engines operating between these temperature limits (TLand TH)
have lower efficiencies. An actual heat engine cannot reach this maximum
theoretical efficiency value because it is impossible to completely eliminate
all the irreversibilities associated with the actual cycle.
Note that TLand THin Eq. 6–18 are absolute temperatures. Using °C or
°F for temperatures in this relation gives results grossly in error.
The thermal efficiencies of actual and reversible heat engines operating
between the same temperature limits compare as follows (Fig. 6–47):

hth• (6–19)

6 hth,rev¬irreversible heat engine

 hth,rev¬reversible heat engine

7 hth,rev¬impossible heat engine

hth,rev 1 

TL

TH

hth 1 

QL

QH

T 1 °C 2 T 1 K 2 273.15

Chapter 6 | 305

273.16 K (assigned)

Water at triple point

T = 273.16

–––QH

QL

Carnot

HE

QH

W

QL

Heat reservoir

T

FIGURE 6–45

A conceptual experimental setup to

determine thermodynamic

temperatures on the Kelvin scale by

measuring heat transfers QHand QL.

Low-temperature reservoir

at TL = 300 K

Carnot

HE

ηth = 70%

QH

Wnet,out

QL

High-temperature reservoir

at TH = 1000 K

FIGURE 6–46

The Carnot heat engine is the most

efficient of all heat engines operating

between the same high- and low-

temperature reservoirs.

SEE TUTORIAL CH. 6, SEC. 10 ON THE DVD.

INTERACTIVE

TUTORIAL