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AIEEE 2004 Physics Solved Paper
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© examsnet.com
Question : 27
Total: 78
Two thermally insulated vessels 1 and 2 are filled with air at temperatures
(
T
1
,
T
2
)
, volume
(
V
1
,
V
2
)
and pressure
(
P
1
,
P
2
)
respectively. If the value joining the two vessels is opened, the temperature inside the vessel at equilibrium will be
T
1
T
2
(
P
1
V
1
+
P
2
V
2
)
/
(
P
1
V
1
T
2
+
P
2
V
2
T
1
)
(
T
1
+
T
2
)
/
2
T
1
+
T
2
T
1
T
2
(
P
1
V
1
+
P
2
V
2
)
/
(
P
1
V
1
T
1
+
P
2
V
2
T
2
)
Validate
Solution:
Here
Q
=
0
and
W
=
0
. Therefore from first law of thermodynamics
∆
U
=
Q
+
W
=
0
∴
Internal energy of the system with partition
=
Internal energy of the system without partition.
n
1
C
v
T
1
+
n
2
C
v
T
2
=
(
n
1
+
n
2
)
C
v
T
∴
T
=
n
1
T
1
+
n
2
T
2
n
1
+
n
2
But
n
1
=
P
1
V
1
R
T
1
and
n
2
=
P
2
V
2
R
T
2
∴
T
=
P
1
V
1
R
T
1
×
T
1
+
P
2
V
2
R
R
2
×
T
2
P
1
V
1
R
R
1
+
R
2
V
2
R
R
R
2
=
T
1
T
2
(
P
1
V
1
+
P
2
V
2
)
P
1
V
1
T
2
+
P
2
V
2
T
1
© examsnet.com
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