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The Quality of Energy

The Carnot heat engine in Example 6–5 receives heat from a source at 925 K
and converts 67.2 percent of it to work while rejecting the rest (32.8 percent)
to a sink at 303 K. Now let us examine how the thermal efficiency varies
with the source temperature when the sink temperature is held constant.
The thermal efficiency of a Carnot heat engine that rejects heat to a sink at
303 K is evaluated at various source temperatures using Eq. 6–18 and is
listed in Fig. 6–49. Clearly the thermal efficiency decreases as the source
temperature is lowered. When heat is supplied to the heat engine at 500
instead of 925 K, for example, the thermal efficiency drops from 67.2 to 39.4
percent. That is, the fraction of heat that can be converted to work drops to
39.4 percent when the temperature of the source drops to 500 K. When the
source temperature is 350 K, this fraction becomes a mere 13.4 percent.
These efficiency values show that energy has qualityas well as quantity.
It is clear from the thermal efficiency values in Fig. 6–49 that more of the
high-temperature thermal energy can be converted to work. Therefore, the
higher the temperature, the higher the quality of the energy(Fig. 6–50).
Large quantities of solar energy, for example, can be stored in large
bodies of water called solar pondsat about 350 K. This stored energy can
then be supplied to a heat engine to produce work (electricity). However,
the efficiency of solar pond power plants is very low (under 5 percent)
because of the low quality of the energy stored in the source, and the con-
struction and maintenance costs are relatively high. Therefore, they are not
competitive even though the energy supply of such plants is free. The tem-
perature (and thus the quality) of the solar energy stored could be raised
by utilizing concentrating collectors, but the equipment cost in that case
becomes very high.
Work is a more valuable form of energy than heat since 100 percent of
work can be converted to heat, but only a fraction of heat can be converted
to work. When heat is transferred from a high-temperature body to a lower-
temperature one, it is degraded since less of it now can be converted to
work. For example, if 100 kJ of heat is transferred from a body at 1000 K to
a body at 300 K, at the end we will have 100 kJ of thermal energy stored at
300 K, which has no practical value. But if this conversion is made through
a heat engine, up to 1 300/1000 70 percent of it could be converted to
work, which is a more valuable form of energy. Thus 70 kJ of work poten-
tial is wasted as a result of this heat transfer, and energy is degraded.

Chapter 6 | 307

That is, this Carnot heat engine converts 67.2 percent of the heat it receives

to work.

(b) The amount of heat rejected QLby this reversible heat engine is easily

determined from Eq. 6–16 to be

Discussion Note that this Carnot heat engine rejects to a low-temperature

sink 164 kJ of the 500 kJ of heat it receives during each cycle.

QL,rev

TL

TH

QH,rev

130  2732 K

1652  2732 K

1 500 kJ 2 164 kJ

Low-temperature reservoir

at TL = 303 K

High-temperature reservoir

at TH

Rev. HE

ηth

TH, K

925

800

700

500

350

ηth, %

67.2

62.1

56.7

39.4

13.4

FIGURE 6–49

The fraction of heat that can be

converted to work as a function of

source temperature (for TL303 K).

2000

1500

1000

500

T, K

Thermal

energy

Quality

FIGURE 6–50

The higher the temperature of the

thermal energy, the higher its quality.