CameraIcon

SearchIcon

MyQuestionIcon

160

You visited us 160 times! Enjoying our articles? Unlock Full Access!

Surface Energy

Under isother...

Question

Under isothermal condition, two soap bubbles of radii $r_{1}$ and $r_{2}$ coalesce to form a single bubble of radius $r$ . The external pressure is $P_{0}$ . Find the surface tension of the soap in terms of the given parameters.

A

\frac{P_{0} (r^{3} - r_{1}^{3} - r_{2}^{3})}{4 (r_{1}^{2} + r_{2}^{2} - r^{2})}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

B

\frac{P_{0} (r^{3} - r_{1}^{3} - r_{2}^{3})}{2 (r_{1}^{2} + r_{2}^{2})}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

\frac{P_{0} r_{1} r_{2}}{(r - r_{1} - r_{2})}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

\frac{2 P_{0} r_{1} r_{2}}{(r - r_{1} - r_{2})}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $\frac{P_{0} (r^{3} - r_{1}^{3} - r_{2}^{3})}{4 (r_{1}^{2} + r_{2}^{2} - r^{2})}$

As the mass (number of moles) of the air is conserved,
$n_{1} + n_{2} = n$

Using ideal gas equation $P V = n R T$ ,

$\frac{P_{1} V_{1}}{R T_{1}}$ + $\frac{P_{2} V_{2}}{R T_{2}}$ = $\frac{P V}{R T}$

Under isothermal condition,

$T_{1} = T_{2} = T$

$\Rightarrow P_{1} V_{1} + P_{2} V_{2} = P V$

Pressure inside the soap bubble is the sum of external pressure and excess pressure inside the soap bubble,

$\Rightarrow (P_{0} + \frac{4 S}{r_{1}}) (\frac{4}{3} π r_{1}^{3}) + (P_{0} + \frac{4 S}{r_{2}}) (\frac{4}{3} π r_{2}^{3}) = (P_{0} + \frac{4 S}{r}) (\frac{4}{3} π r^{3})$

$\Rightarrow S = \frac{P_{0} (r^{3} - r_{1}^{3} - r_{2}^{3})}{4 (r_{1}^{2} + r_{2}^{2} - r^{2})}$

Hence, option $(A)$ is correct.

Suggest Corrections

thumbs-up

1

Similar questions

Q. Two spherical soap bubbles of a radii

r_{1}

r_{2}

in vacuum coalesce under isothermal conditions. The resulting bubble has the radius

R

Q. Two soap bubbles of radii

a

b

combine under isothermal conditions to form a single bubble of radius

c

without any leakage of air. If

P_{0} =

atmospheric pressure and

T =

surface tension of soap solution, show that

P_{0} = \frac{4 T (a^{2} + b^{2} - c^{2})}{c^{3} - a^{3} - b^{3}}

Q. Two soap bubbles each with radius

r_{1}

r_{2}

coalesce in vacuum under isothermal conditions to form a bigger bubble of radius R.Then, R is equal to

Q. Two soap bubbles of radii 4 cm and 3 cm respectively coalesce under isothermal conditions to form a single bubble. What is the radius of the new single bubble?

Q. If two soap bubbles of different radii

r_{1}

r_{2}

r_{1} > r_{2}

)coalesce to form a single double bubble having a common surface, then the radius of curvature of the interface is given by

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Surface Tension

PHYSICS

Watch in App

explore_more_icon

Explore more

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon