9.
An air bubble starts rising from the bottom of a lake. Its diameter 3.6 mm at the bottom and 4 mm
at the surface. The depth of the lake is 250 cm and temperature at the surface is 40°C. Then the
temperature at the bottom of the lake is (Neglect surface tension effect) (Given g = 980 cm/sec)
(A) 11.2°C
(C) 10.36°C
(D) 25°C
(B) 0°C
Answers
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11th
Physics
Thermodynamics
Thermodynamic Processes
An air bubble starts rising...
PHYSICS
An air bubble starts rising from the bottom of a lake. Its diameter is 3.6mm at the bottom and 4mm at the surface. The depth of the lake is 250cm and the temperature at surface is 40
o
C.
What is the temperature at the bottom of the lake? Given atmospheric pressure =76cm of Hg and g=980cm/s
2
.
ANSWER
At the bottom of the lake, volume of the bubble
V
1
=
3
4
πr
3
=
3
4
π(0.18)
3
Pressure on the bubble, p
1
= atmospheric pressure + pressure due to a column of 250cm of water.
=76×13.6×980+250×1×980
=(76×13.6+250)980dyne/cm
2
At the surface of the lake, volume of the bubble
V
2
=
3
4
πr
2
3
=
3
4
π(0.2)
3
cm
3
Pressure on the bubble,
p
2
= atmospheric pressure
=(76×13.6×980)dyne/cm
2
T
2
=273+40=313K
Now,
T
1
p
1
V
1
=
T
2
p
2
V
2
⇒
T
1
(76×13.6×250)980×(
3
4
)π(0.18)
3
=
313
(76×13.6)×980(
3
4
)π(0.2)
3
⇒T
1
=283.37K
∴T
1
=283.37−273=10.37
o
C.