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()
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
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 K
57.0 C
330 K.
f
T
⋅°
+
⋅
°
=
⋅+
⋅
=°
=
(b) Now temperatures must be given in Kelvins:
T
ai
= 393 K,
T
wi
= 293 K, and
T
f
= 330 K.
For the aluminum,
dQ = m
a
c
a
dT
and the change in entropy is
(
)
330 K
ln
0.200 kg 900 J/kg K ln
373 K
22.1 J/K.
f
ai
T
f
aa
a
a
a
T
ai
T
dQ
dT
Sm
c
m
c
TT
T
§·
Δ=
=
=
=
⋅
¨¸
©¹
=−
³³
(c) The entropy change for the water is
330K
ln
(0.0500 kg)(4190 J kg.K)ln
293K
24.9J K.
f
wi
T
f
ww
w
w
w
T
wi
T
dQ
dT
c
m
c
T
=
=
=
=+
(d) The change in the total entropy of the aluminumwater system is
Δ
S =
Δ
S
a
+
S
w
=
−
22.1 J/K + 24.9 J/K = +2.8 J/K.
7. (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 specific heat of aluminum,
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This note was uploaded on 06/03/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.
 Spring '08
 Any
 Physics, Energy, Mass, Heat

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