Derive an expression for excess of pressure inside a soap bubble. from Physics Mechanical Properties of Fluids Class 11 Manipur Board
Zigya Logo

Chapter Chosen

Mechanical Properties of Fluids

Book Chosen

Physics Part II

Subject Chosen

Physics

Book Store

Download books and chapters from book store.
Currently only available for.
CBSE Gujarat Board Haryana Board

Previous Year Papers

Download the PDF Question Papers Free for off line practice and view the Solutions online.
Currently only available for.
Class 10 Class 12
Derive an expression for excess of pressure inside a soap bubble.

Consider a soap bubble of radius R and surface tension T.

There are two free surfaces of soap bubble. Due to surface tension the molecules on the surface film experience the net force in inward direction normal to the surface.

Therefore there is more pressure inside than outside.

Let pi be pressure inside the liquid drop and po the pressure outside the drop.

Therefore excess of pressure inside the liquid drop is,

                     p =p1–Po




Due to excess of pressure inside the liquid drop, the free surface of the drop will experience the net force in outward direction due to which the drop expands.

Let the free surface be displaced by dR under isothermal conditions.

Therefore excess of pressure does the work in displacing the surface and that work will be stored in the form of potential energy.

The work done by excess of pressure in displacing the surface is,

dW= Force x displacement 

     = (excess of pressure x Surface area) x displacement of surface

    italic equals p italic cross times italic 4 pi R to the power of italic 2 cross times dR space space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis 1 right parenthesis 

Increase in the potential energy is given by, 

dU = surface tension x increase in area of the free surface

    
equals space straight T space open square brackets 2 open parentheses 4 straight pi open parentheses straight R plus dR squared close parentheses minus 4 πR squared close parentheses close square brackets
equals space straight T space open square brackets 2 open curly brackets 4 straight pi open parentheses 2 RdR close parentheses close curly brackets close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space... left parenthesis 2 right parenthesis

From (1) and (2)

   straight p cross times 4 πR squared cross times dR equals space straight T left square bracket space 2 space left curly bracket 4 straight pi left parenthesis 2 RdR space right parenthesis space right curly bracket space right square bracket
rightwards double arrow space space space space space space space space space space space space space space space space straight p space equals space fraction numerator 4 straight T over denominator straight R end fraction

p is the excess of pressure inside a soap bubble. 

2675 Views

Do intermolecular or inter-atomic forces follow inverse square law?

No. Intermolecular and inter-atomic forces do not obey the inverse square law. 
1257 Views

Why solids have definite shape while liquids do not have definite shape?

Solids: Intermolecular forces are very strong and thermal agitations are not sufficiently strong to separate the molecules from their mean position. Solids are rigid and hence they have definite shapes.
Liquids: In liquids intermolecular forces are not sufficiently strong to hold the molecules at definite sites, as a result they move freely within the bulk of liquid, therefore, do not possess definite shapes. Liquids take the same shape as that of the container. 
977 Views

What is hydrodynamics?

Hydrodynamics is the branch of science that studies about the force exerted by the fluids or acting on the fluids. 
799 Views

What is fluid?

Any material that can flow is a fluid. Liquids and gases are examples of fluid.


976 Views

What is hydrostatics?

Hydrostatics is the branch of fluid mechanics that studies incompressible fluids at rest. The study of fluids at rest or objects placed at rest in fluids is hydrostatics.
854 Views