Version PREVIEW – HW 10 (solution is available) – Savrasov – (39824)
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Serway CP 12 33
001
10.0 points
A nuclear power plant has an electrical power
output of 1333 MW and operates with an
efficiency of 33%.
If excess energy is carried away from the
plant by a river with a flow rate of 1
×
10
6
kg
/
s,
what is the rise in temperature of the flowing
water?
Correct answer: 0
.
646535
◦
C.
Explanation:
Given :
P
output
= 1333 MW = 1
.
333
×
10
9
W
,
e
= 0
.
33
,
and
Δ
m
Δ
t
= 1
×
10
6
kg
/
s
.
The Carnot efficiency is
e
=
W
Q
h
and
P
=
W
t
=
e
c
Q
h
t
Q
h
=
P t
e
.
From
e
=
Q
h

Q
c
Q
h
, the energy expelled in
time
t
is
Q
c
=
Q
h
(1

e
) =
P t
e
(1

e
)
=
P t
parenleftbigg
1
e

1
parenrightbigg
.
In time
t
, the mass of cooling water used is
m
=
Δ
m
Δ
t
·
t ,
so its rise in temperature is
Δ
T
=
Q
c
m c
=
P t
Δ
m
Δ
t
t c
parenleftbigg
1
e

1
parenrightbigg
=
P
Δ
m
Δ
t
c
parenleftbigg
1
e

1
parenrightbigg
=
1
.
333
×
10
9
W
(1
×
10
6
kg
/
s) (4186 J
/
kg
·
◦
C)
×
parenleftbigg
1
0
.
33

1
parenrightbigg
=
0
.
646535
◦
C
.
Temperature Increase
002
10.0 points
The efficiency of a 1232 MW nuclear power
plant is 38
.
4%.
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 Fall '09
 RichardScalettar
 Power, Heat, Nuclear power plant, Trigraph, Correct Answer, Carnot cycle

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