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9. (a) The energy that leaves the aluminum as heat has magnitude
Q
=
m
a
c
a
(
T
ai
−
T
f
), where
m
a
is
the mass of the aluminum,
c
a
is the speciFc heat of aluminum,
T
ai
is the initial temperature of the
aluminum, and
T
f
is the Fnal temperature of the aluminumwater system. The energy that enters
the water as heat has magnitude
Q
=
m
w
c
w
(
T
f
−
T
wi
), where
m
w
is the mass of the water,
c
w
is
the speciFc heat of water, and
T
wi
is the initial temperature of the water. The two energies are the
same in magnitude since no energy is lost. Thus,
m
a
c
a
(
T
ai
−
T
f
)=
m
w
c
w
(
T
f
−
T
wi
⇒
T
f
=
m
a
c
a
T
ai
+
m
w
c
w
T
wi
m
a
c
a
+
m
w
c
w
.
The speciFc heat of aluminum is 900 J
/
kg
·
K and the speciFc heat of water is 4190 J
/
kg
·
K. Thus,
T
f
=
(0
.
200 kg)(900 J
/
kg
·
K)(100
◦
C) + (0
.
0500 kg)(4190 J
/
kg
·
K)(20
◦
C)
(0
.
200 kg)(900 J
/
kg
·
K) + (0
.
0500 kg)(4190 J
/
kg
·
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This note was uploaded on 11/12/2011 for the course PHYS 2001 taught by Professor Sprunger during the Fall '08 term at LSU.
 Fall '08
 SPRUNGER
 Physics, Energy, Mass, Heat

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