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EAMCET Engineering 2006 Solved Paper
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© examsnet.com
Question : 14
Total: 160
Two soap bubbles combine to form a single bubble. In this process, the change in volume and surface area are respectively
V
and
A
. If
P
is the atmospheric pressure, and
T
is the surface tension of the soap solution, the following relation is true :
4
P
V
+
3
T
A
=
0
3
P
V
−
4
T
A
=
0
4
P
V
−
3
T
A
=
0
3
P
V
+
4
T
A
=
0
Validate
Solution:
Let radii of two soap bubbles are
a
and
b
respectively and radius of single larger bubble is
c
.
As excess pressure for a soap bubble is
4
T
r
and external pressure
P
.
P
i
=
P
+
4
T
r
So,
P
a
=
P
+
4
T
a
,
P
b
=
P
+
4
T
b
and
P
c
=
P
+
4
T
c
. . . (i)
and
V
a
=
4
3
π
a
3
,
V
b
=
4
3
π
b
3
and
V
c
=
4
3
π
c
3
. . . (ii)
Now as mass is conserved.
µ
a
+
µ
b
=
µ
c
i.e.,
P
a
V
a
R
T
a
+
P
b
V
b
R
T
b
=
P
c
V
c
R
T
c
(
as
P
V
=
µ
R
T
)
As temperature is constant, i.e.,
T
a
=
T
b
=
T
c
So,
P
a
V
a
+
P
b
V
b
=
P
c
V
c
which in the light of Eqs. (i) and (ii) becomes,
(
P
+
4
T
a
)
(
4
3
π
a
3
)
+
(
P
+
4
T
b
)
(
4
3
π
b
3
)
=
(
P
+
4
T
c
)
(
4
3
π
c
3
)
i.e.,
4
T
(
a
2
+
b
2
−
c
2
)
=
P
(
c
3
−
a
3
−
b
3
)
. . . (iii)
Now,
V
=
4
3
π
(
a
3
+
b
3
−
c
3
)
and
A
=
4
π
(
a
2
+
b
2
−
c
2
)
∴
T
A
π
=
−
3
4
π
V
P
or
4
T
A
+
3
P
V
=
0
© examsnet.com
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