CHAPTER
21
HEAT,
WORK,
AND
THE
FIRST
LAW
OF
THERMODYNAMICS
ActivPhysics
can help with these problems:
Activities 8.58.13
Section 211:
The
First Law of
Thermodynamics
Problem
1. In a perfectly insulated container, 1.0 kg of water
is stirred vigorously until its temperature rises by
7.0°C. How much work was done on the water?
Solution
Since the container is perfectly insulated thermally, no
heat enters or leaves the water in it. Thus, Q
=
0 in
Equation 211. The change in the internal energy of
the water is determined from its temperature rise,
AU
=
rnc
AT
(see comments in Section
194
on
internal energy), so
W
=
AW
=
(1
kg) x
(4.184 kJ/kg.K)(7 K)
=
29.3 kJ. (The negative sign
signifies that work
was
done on the water.)
Problem
5.
The most efficient largescale electric power
generating systems use hightemperature
gas
turbines and a socalled combined cycle system that
maximizes the conversion of thermal energy into
useful work. One such plant produces electrical
energy at the rate of 360 hlW, while extracting
energyfrom its natural
gas
fuel at the rate of
670
MW.
(a) At what rate does it reject waste heat
to the environment?
(b)
Find its efficiency, defined
as
the percent of the total energy extracted from
the fuel that ends
up
as
work.
Solution
(a) If we assume that the generating system operates
in a cycle and choose it
as
"the system," then dli/dt
=
0
and Equation 212 implies dQ/dt
=
dW/dt. Here,
dW/dt is the rate that the generator supplies energy to
its surroundings (360
h/lW
in this problem) and dQ/dt
is the net rate of heat flow into the generator from the
surroundings. Since the system is just the generator,
the net heat flow is the difference between
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 Spring '05
 wurthmeir
 Thermodynamics, Work, First Law Of Thermodynamics, Heat

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