Excess Pressure: Definition, Formula and Examples

Excess Pressure

Edited By Vishal kumar | Updated on Jul 02, 2025 05:33 PM IST

Ever blown a soap bubble and then stopped to wonder why it holds its shape, or why small droplets of water are spherical? The reason for all phenomena lies in the concept of excess pressure. The excess pressure is additional pressure inside a liquid drop or a soap bubble as compared to the outside. The difference in pressure is caused by surface tension, a force that acts along the surface of a liquid, causing it to contract and minimize its surface area. Understanding excess pressure sheds light on these phenomena of liquid drops, bubbles, and many other fluid dynamics.

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What is Excess Pressure
Solved Example Based on Excess Pressure
Summary

Excess Pressure

This article will cover the concept of Excess pressure inside a liquid drop & soap bubble. This is the part of chapter Properties of Solids and Liquids which is a crucial chapter in Class 11 physics. It is not only crucial for board exams but also for competitive exams like the Joint Entrance Examination (JEE Main), National Eligibility Entrance Test (NEET), and other entrance exams such as SRMJEE, BITSAT, WBJEE, BCECE and more. Over the last ten years of the JEE Main and NEET(from 2013 to 2023), a total of ten questions have been asked on this concept.

What is Excess Pressure

The difference in pressure between the two sides of the liquid surface is known as Excess Pressure.

Cause of Excess Pressure

Drop or bubble tends to contract and so compresses the matter enclosed, due to the property of surface tension. Thus to prevent further contraction, internal pressure inside the Drop or bubble increases. This internal pressure increases until the equilibrium is achieved. So that is why in equilibrium the pressure inside a bubble or drop is greater than outside. And this difference of pressure between the two sides of the liquid surface is called excess pressure.

Excess Pressure in Different Cases

Excess pressure for plane surface

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ΔP=0

means no difference in pressure.

Excess pressure for concave surface

ΔP=2TR

Where,

T- Surface Tension

R- Radius

Excess pressure for a convex surface

ΔP=2TR

Pressure Difference in Water Droplet

ΔP=2TR

Change in Pressure of bubble in the air

ΔP=(2TR)×2=4TR

Excess pressure is inversely proportional to the radius of the bubble (or drop).

Solved Example Based on Excess Pressure

Example 1: A small soap bubble of radius 4 cm is trapped inside another bubble of radius 6 cm without any contact. Let p2 be the pressure inside the inner bubble and p0, the pressure outside the outer bubble. The radius (in cm ) of another bubble with a pressure difference p2−p0 between its inside and outside would be :

1) 12

2) 2.4

3) 6

4) 4.8

Solution:

Change in Pressure of bubble in air -

ΔP=(2TR)×2=4TR

- wherein

T- Surface tension

R- Radius

p2−p1=4sR1p1−p0=4sR2p2−p0=4s(1R1+1R2)1R=1R1+1R2R=R1R2R1+R2=4∗64+6 cm=2.4 cm

Hence, the answer is option (2).

Example 2: Two soap bubbles coalesce to form a single bubble. If V is the subsequent change in the volume of contained air and S the change in total surface area, T is the surface tension and P is atmospheric pressure, which of the following relations is correct?

1) 4PV+3ST=0
2) 3PV+4ST=0
3) 2PV+3ST=0
4) 3PV+2ST=0

Solution:

Change in Pressure of bubble in air -

ΔP=(2TR)×2=4TR

- wherein

T- Surface tension

R- Radius

(P+4Tr1)(4π3r13)+(P+4Tr2)4π3r23=(P+4Tr)4π3r3PV+4T3(4πr12+4πr22−4πr2)=0⇒3PV+4TS=0

Hence, the answer is option (2).

Example 3: A soap bubble of radius 3 cm is formed inside another soap bubble of radius 6 cm. The radius of an equivalent soap bubble which has the same excess pressure as inside the smaller bubble with respect to the atmospheric pressure is -------- cm.

1) 2

2) 8

3) 4

4) 1

Solution:

R=3 cm=3×10−2 m

p1−p2=4Tr1→(1)p2−p0=4Tr2→(2)p′−p0=4Tr→(3)∵p1−p0=p′−p0 (Given) 4Tr1+4Tr2=4Tr13+16=1r918=1rr=2 cm

Hence, the answer is option (1).

Example 4: There is an air bubble of radius 1.0 mm in a liquid of surface tension 0.075 nm−1 and density 1000 kg m−1 at a depth of 10 cm below the free surface. The amount by which the pressure inside the bubble is greater than the atmospheric pressure is Pa___.(g=10 ms−2)

1)1170

2)1140

3)1150

4)1160

Solution:

Pin =P0+ρgh+2Tr

Pin −P0=1000×10×0.1+2×0.0750.001=1000+150Pin −P0=1150 Pa

Hence, the answer is option (3).

Example 5: Which of the following relations is correct? ( P₁ =pressure inside drop, P₂ = pressure outside drop).

1) )P1−P2=2TR
2) P2−P1=2TR
3) P1−P2=4TR
4) P2−P1=4TR

Solution:

Excess pressure for the drop :

ΔP=2TR
P1>P2 (pressure inside is higher than the pressure outside)
P1−P2=2TR

Hence, the answer is option (1).

Summary

The excess pressure is additional pressure inside a liquid drop or a soap bubble as compared to the outside. The difference in pressure is caused by surface tension, a force that acts along the surface of a liquid, causing it to contract and minimize its surface area. Understanding excess pressure sheds light on these phenomena of liquid drops, bubbles, and many other fluid dynamics.

Frequently Asked Questions (FAQs)

1. What is excess pressure?

Excess pressure is the additional pressure inside a curved liquid surface compared to the pressure outside. It occurs due to surface tension and is responsible for the spherical shape of liquid droplets and bubbles.

2. Why do small water droplets have higher excess pressure than larger ones?

Small water droplets have higher excess pressure because the surface tension force acts over a smaller surface area. As the droplet size decreases, the curvature increases, leading to greater excess pressure according to the Young-Laplace equation.

3. How does excess pressure relate to the shape of soap bubbles?

Excess pressure causes soap bubbles to form a spherical shape. The pressure inside the bubble is slightly higher than outside, and surface tension acts to minimize the surface area, resulting in a perfect sphere when the bubble is free-floating.

4. Can excess pressure be negative?

No, excess pressure cannot be negative. It is always positive or zero. Negative excess pressure would imply that the pressure inside a curved surface is less than the outside pressure, which is not possible under normal conditions.

5. What is the Young-Laplace equation, and how does it relate to excess pressure?

The Young-Laplace equation describes the relationship between excess pressure, surface tension, and the curvature of a liquid surface. It states that excess pressure is directly proportional to surface tension and inversely proportional to the radius of curvature.

6. How does excess pressure affect the boiling point of liquids in small droplets?

Excess pressure increases the boiling point of liquids in small droplets. The higher pressure inside the droplet requires more energy to overcome, resulting in a slightly higher temperature needed for the liquid to boil compared to its bulk form.

7. Why do water striders not sink when walking on water?

Water striders don't sink due to surface tension and excess pressure. Their legs create small depressions in the water surface, which increases the excess pressure in those areas. This pressure, combined with the insect's light weight, keeps it afloat.

8. How does excess pressure contribute to capillary action?

Excess pressure plays a role in capillary action by creating a pressure difference between the curved liquid surface in a capillary tube and the flat surface outside. This pressure difference, along with adhesive forces, causes the liquid to rise in the tube.

9. What is the relationship between excess pressure and the Laplace pressure?

Excess pressure and Laplace pressure are the same concept. The term "Laplace pressure" is often used in honor of Pierre-Simon Laplace, who first described this phenomenon mathematically. Both terms refer to the pressure difference across a curved liquid surface.

10. How does excess pressure affect the formation of raindrops?

Excess pressure influences raindrop formation by determining the maximum size of stable water droplets in the air. As droplets grow, the excess pressure decreases, allowing them to merge with other droplets until they become heavy enough to fall as rain.

11. Can excess pressure explain why mercury forms a convex meniscus in a glass tube?

Yes, excess pressure contributes to mercury's convex meniscus. The cohesive forces between mercury molecules are stronger than the adhesive forces with glass, creating an outward curved surface. This curvature results in excess pressure that maintains the convex shape.

12. How does temperature affect excess pressure in a soap bubble?

Temperature affects excess pressure in a soap bubble by changing the surface tension of the soap solution. As temperature increases, surface tension generally decreases, leading to a reduction in excess pressure. This can cause the bubble to expand slightly.

13. What role does excess pressure play in the formation of dew drops?

Excess pressure helps maintain the spherical shape of dew drops. As water vapor condenses on surfaces, the drops remain small due to surface tension. The excess pressure inside these tiny droplets contributes to their stability and characteristic round shape.

14. How does excess pressure relate to the concept of vapor pressure?

Excess pressure affects vapor pressure by increasing the pressure inside small liquid droplets. This increased pressure raises the vapor pressure of the liquid in the droplet compared to its bulk form, making it slightly harder for molecules to escape into the gas phase.

15. Why don't large raindrops split into smaller ones due to excess pressure?

Large raindrops don't split due to excess pressure because as droplet size increases, excess pressure decreases. Other forces like air resistance and surface tension become more dominant, shaping the drop into a flattened sphere rather than causing it to split.

16. How does excess pressure affect the process of coalescence in emulsions?

Excess pressure plays a role in coalescence by creating a pressure difference between droplets of different sizes in an emulsion. Smaller droplets with higher excess pressure tend to merge with larger ones, leading to the gradual separation of the emulsion over time.

17. Can excess pressure explain why water beads up on a hydrophobic surface?

Yes, excess pressure contributes to water beading on hydrophobic surfaces. The lack of attraction between water and the surface causes the water to minimize its contact area, forming droplets. The excess pressure inside these droplets helps maintain their rounded shape.

18. How does the concept of excess pressure apply to lung alveoli?

In lung alveoli, excess pressure helps prevent collapse. The curved surface of alveoli creates a slight excess pressure inside, which, combined with surfactants that reduce surface tension, keeps these tiny air sacs open and functional during breathing.

19. What is the relationship between excess pressure and the critical radius in nucleation processes?

The critical radius in nucleation is the minimum size a nucleus must reach to become stable. Excess pressure plays a crucial role here, as it determines the pressure difference between the nucleus and its surroundings. Nuclei smaller than the critical radius have too high an excess pressure and tend to dissolve.

20. How does excess pressure affect the stability of foams?

Excess pressure influences foam stability by creating pressure differences between bubbles of different sizes. Smaller bubbles with higher excess pressure tend to shrink and eventually disappear, while larger bubbles grow. This process, known as Ostwald ripening, leads to the gradual coarsening of foam structure over time.

21. Can excess pressure explain why oil and water don't mix?

While excess pressure doesn't directly cause oil and water to separate, it contributes to the stability of the interface between them. The curved interface between oil and water droplets creates excess pressure, which, along with surface tension and density differences, helps maintain the separation between the two liquids.

22. How does excess pressure relate to the phenomenon of supersaturation?

Excess pressure plays a role in supersaturation by affecting the solubility of gases in liquids. The increased pressure inside small bubbles makes it more difficult for dissolved gases to form new bubbles, allowing a liquid to hold more dissolved gas than it normally would under standard conditions.

23. What is the significance of excess pressure in the formation of cloud droplets?

Excess pressure is crucial in cloud droplet formation. It affects the equilibrium vapor pressure around tiny water droplets, influencing their growth or evaporation. This process, described by the Kelvin equation, helps explain why cloud droplets require condensation nuclei to form and grow.

24. How does excess pressure contribute to the phenomenon of cavitation?

Excess pressure is relevant to cavitation as it affects the formation and collapse of vapor bubbles in a liquid. When local pressure drops below the vapor pressure, bubbles form. As they move to higher pressure regions, the excess pressure inside the bubbles decreases rapidly, leading to violent collapse and potential damage to surfaces.

25. Why does a soap film between two circular rings take on a catenoid shape?

A soap film between circular rings forms a catenoid shape to minimize its surface area while maintaining constant mean curvature. This shape ensures that the excess pressure is uniform across the entire surface, resulting in a stable configuration that balances surface tension forces.

26. How does excess pressure affect the process of distillation?

Excess pressure influences distillation by affecting the boiling points of liquids in small droplets. The increased pressure inside these droplets slightly raises their boiling points, which can impact the efficiency and purity of the distillation process, especially in systems involving fine mists or aerosols.

27. What role does excess pressure play in the formation of liquid bridges between particles?

Excess pressure is crucial in liquid bridge formation between particles. It creates a pressure difference between the curved surface of the liquid bridge and the surrounding air, contributing to the cohesive forces that hold particles together. This phenomenon is important in soil mechanics and powder technology.

28. How does excess pressure relate to the concept of Ostwald ripening in emulsions?

Excess pressure drives Ostwald ripening in emulsions. Smaller droplets have higher excess pressure, leading to a higher solubility of the dispersed phase. This causes material to diffuse from smaller to larger droplets over time, resulting in the growth of larger droplets at the expense of smaller ones.

29. Can excess pressure explain why some insects can walk on water but sink when detergent is added?

Yes, excess pressure contributes to this phenomenon. Water's high surface tension creates sufficient excess pressure to support light insects. When detergent is added, it reduces surface tension, lowering the excess pressure. This decreased pressure is no longer enough to support the insect's weight, causing it to sink.

30. How does excess pressure affect the process of bubble nucleation in carbonated beverages?

Excess pressure plays a crucial role in bubble nucleation in carbonated drinks. It affects the critical radius for bubble formation. Nucleation sites with high curvature (like scratches or impurities) reduce the excess pressure needed for bubble formation, making it easier for bubbles to nucleate and grow in these locations.

31. What is the relationship between excess pressure and the shape of a pendant drop?

The shape of a pendant drop is determined by the balance between gravitational forces and surface tension, which creates excess pressure. The excess pressure varies along the drop's surface due to changing curvature, resulting in the characteristic teardrop shape as the drop elongates under its own weight.

32. How does excess pressure contribute to the phenomenon of superheating in liquids?

Excess pressure is relevant to superheating as it affects bubble nucleation. In a pure, smooth container, the lack of nucleation sites means that bubbles must form spontaneously, requiring very high excess pressure. This allows the liquid to be heated above its normal boiling point without boiling, leading to superheating.

33. Can excess pressure explain why small bubbles rise more slowly in a liquid than larger ones?

Yes, excess pressure contributes to this effect. Smaller bubbles have higher excess pressure, which makes them more rigid and spherical. This increased rigidity, combined with their smaller size, results in higher drag forces relative to their buoyancy, causing them to rise more slowly than larger, more deformable bubbles.

34. How does excess pressure affect the process of sintering in powder metallurgy?

In sintering, excess pressure plays a role in the formation of necks between powder particles. The curved surfaces of these necks create pressure differences that drive mass transport, contributing to the densification process. Understanding this helps in optimizing sintering conditions for different materials.

35. What is the significance of excess pressure in the formation of aerosols?

Excess pressure is crucial in aerosol formation and stability. It affects the size distribution of droplets, their evaporation rates, and their tendency to coalesce. Smaller droplets with higher excess pressure are more prone to evaporation, influencing the overall behavior and lifespan of the aerosol.

36. How does excess pressure relate to the concept of capillary condensation?

Excess pressure is key to capillary condensation. In narrow pores or between closely spaced particles, the curved liquid-vapor interface creates an excess pressure that lowers the vapor pressure required for condensation. This allows condensation to occur at relative humidities below 100%, affecting phenomena like adsorption and soil water retention.

37. Can excess pressure explain the formation of sessile drops on surfaces?

Yes, excess pressure contributes to sessile drop formation. The balance between surface tensions at the solid-liquid-vapor interface and the excess pressure inside the drop determines its shape. This balance results in a specific contact angle, which characterizes the wetting behavior of the liquid on the surface.

38. How does excess pressure affect the stability of thin films, such as in soap bubbles?

Excess pressure influences thin film stability by creating a pressure difference across the film. In soap bubbles, this pressure difference tends to drive liquid from thinner to thicker regions of the film. This effect, combined with surface tension and evaporation, determines the film's lifetime and stability.

39. What role does excess pressure play in the phenomenon of liquid jet breakup?

Excess pressure is crucial in liquid jet breakup. As the jet emerges, surface perturbations create regions of different curvature, leading to pressure variations along the jet's surface. These pressure differences, driven by excess pressure, grow over time and eventually cause the jet to break into droplets.

40. How does excess pressure contribute to the formation of fog and mist?

Excess pressure affects fog and mist formation by influencing the stability and growth of tiny water droplets in the air. The high excess pressure in these small droplets increases their equilibrium vapor pressure, affecting their tendency to grow or evaporate and thus impacting the overall formation and persistence of fog and mist.

41. Can excess pressure explain why water droplets bounce on extremely hot surfaces?

Yes, excess pressure contributes to this phenomenon, known as the Leidenfrost effect. When a droplet contacts an extremely hot surface, it creates a vapor layer underneath. The excess pressure inside the droplet, combined with this vapor cushion, helps maintain the droplet's shape and contributes to its ability to bounce and move on the hot surface.

42. How does excess pressure relate to the concept of nucleation in phase transitions?

Excess pressure is crucial in nucleation processes. For a new phase to form (e.g., a liquid droplet in supersaturated vapor), it must overcome the excess pressure created by its curved surface. This pressure barrier contributes to the activation energy required for nucleation, affecting the rate and likelihood of phase transitions.

43. What is the significance of excess pressure in the formation of plant xylem embolisms?

Excess pressure plays a role in xylem embolism formation. When water tension in xylem vessels becomes too high, air bubbles can nucleate. The excess pressure inside these bubbles, if greater than the surrounding liquid pressure, can cause the bubbles to expand, potentially blocking water transport in the plant.

44. How does excess pressure affect the behavior of nanobubbles in liquids?

Excess pressure significantly influences nanobubble behavior. According to classical theory, the extremely high excess pressure in nanobubbles should cause them to dissolve almost instantly. Their observed stability challenges this view, leading to ongoing research into surface effects and gas dynamics at the nanoscale.

45. Can excess pressure explain why some liquids form drops while others spread on surfaces?

Yes, excess pressure contributes to this behavior. Liquids that form drops have strong cohesive forces, creating high surface tension and significant excess pressure in the drops. Liquids that spread have weaker cohesive forces relative to their adhesion to the surface, resulting in lower excess pressure and a tendency to maximize contact area.

46. How does excess pressure relate to the phenomenon of sonoluminescence?

Excess pressure is crucial in sonoluminescence. As sound waves create and collapse tiny bubbles in a liquid, the rapid increase in pressure and temperature inside the bubble is partly due to the extreme excess pressure at the final stages of collapse. This contributes to the emission of light observed in this phenomenon.

47. What role does excess pressure play in the formation of ocean spray and sea salt aerosols?

Excess pressure influences ocean spray formation by affecting the size and stability of water droplets created by breaking waves. It also plays a role in the formation of sea salt aerosols as these droplets evaporate, influencing the size distribution and lifetime of the resulting salt particles in the atmosphere.

48. How does excess pressure contribute to the phenomenon of liquid bridges in atomic force microscopy?

In atomic force microscopy, excess pressure in liquid bridges between the tip and sample surface affects the force experienced by the probe. The curvature of these nanoscale bridges creates significant excess pressure, contributing to the attractive forces that influence measurement accuracy and imaging resolution.

49. Can excess pressure explain the formation of micelles in surfactant solutions?

While excess pressure isn't the primary driver of micelle formation, it does play a role. The curved surface of micelles creates an excess pressure inside, which is balanced by the hydrophobic effect and electrostatic interactions. This pressure contributes to the overall energetics and stability of micellar structures.

50. How does excess pressure affect the process of membrane filtration and reverse osmosis?

Excess pressure is relevant in membrane processes, particularly for pores or channels approaching molecular dimensions. The curvature of liquid interfaces in these small spaces creates excess pressure that can affect the chemical potential of the solution, influencing transport rates and separation efficiencies in filtration and reverse osmosis systems.