JEE · Physics
Explain surface tension from molecular attraction, apply surface energy and excess pressure relations to drops and bubbles, use angle of contact and wetting to predict capillary behaviour, and diagnose why a surface tension solution goes wrong.
Content status: draft. Verified academic content for this page has not been loaded yet, so the page is excluded from search indexing and the sitemap.
In short
Surface tension is the tendency of a liquid surface to behave like a stretched elastic membrane, caused by unbalanced intermolecular attraction on molecules at the surface compared with molecules inside the bulk liquid. It is measured as force per unit length along the surface, and equivalently as surface energy per unit area.
A correct solution identifies how many free surfaces are involved, whether the shape is a drop or a bubble, what the angle of contact tells you about wetting, and whether temperature or an added impurity is changing the surface tension value itself before any pressure or capillary rise formula is applied.
The official JEE documents define content scope. They do not publish chapter weightage, so none is asserted here.
Verified against the current JEE Main 2026 syllabus and JEE Advanced 2026 syllabus. This is a wording and scope mapping, not a claim about question difficulty or frequency.
Sources: JEE Main 2026 syllabus and JEE (Advanced) 2026 syllabus, both linked in the sources section below. Viscosity, Stokes' law, terminal velocity, streamline flow and Bernoulli's theorem sit in the same official unit but are treated on the Fluid Mechanics page on this site.
Prerequisite
Units and Measurements
Stabilise units and dimensional consistency before surface tension formulas.
Prerequisite
Elasticity
Understand stress, strain and elastic energy of solids before surface energy of liquids.
Parent
JEE Physics
Subject hub for the Physics chapter set.
Parent
JEE syllabus
Exam-level official scope for every Physics, Chemistry and Mathematics unit.
This is a readiness check, not a weightage or scoring-priority list.
You should be able to:
A molecule inside the bulk liquid is pulled equally in all directions; a molecule at the surface has neighbours only on the liquid side, producing a net inward pull that resists surface expansion.
Molecules inside a liquid are surrounded by neighbours on every side, so their net intermolecular force averages to zero. Molecules at the free surface have liquid neighbours only below and beside them, so they experience a net inward pull. Increasing surface area means moving more molecules to this less favourable surface position, which requires work.
Surface tension equals work done per unit increase in surface area at constant temperature.
Because increasing surface area requires work against the inward molecular pull, surface tension can be expressed either as force per unit length along a line on the surface, or as surface energy per unit area. Both descriptions are numerically equal and physically consistent.
A curved liquid surface under tension supports a pressure difference between its concave and convex sides. The excess pressure on the concave side increases as the radius of curvature decreases, which is why smaller drops and bubbles sustain a larger excess pressure than larger ones of the same liquid.
A liquid drop has one free surface; a soap bubble in air has two free surfaces.
A liquid drop or a cavity inside a liquid has a single liquid-air interface. A soap bubble in air has an inner and an outer liquid film surface, so its excess pressure relation carries an extra factor compared with a drop of the same radius and surface tension.
The angle of contact is decided by the liquid, the solid surface and the surrounding medium together, not by the liquid alone.
The angle of contact is the angle measured inside the liquid between the solid surface and the tangent to the liquid surface at the point of contact. A liquid that wets a solid has an acute angle of contact and a concave meniscus; a liquid that does not wet a solid has an obtuse angle of contact and a convex meniscus.
In a narrow tube, the curved meniscus produced by the angle of contact creates a pressure difference that pushes the wetting liquid up the tube until the weight of the raised liquid column balances that pressure difference. A non-wetting liquid is depressed in the tube instead of rising.
Surface tension of a liquid generally decreases as temperature rises, because increased molecular agitation weakens the net inward attraction at the surface, and it becomes zero at the critical temperature. Dissolved impurities can raise or lower surface tension depending on the specific solute and liquid, so this effect is read from the given data rather than assumed in one direction.
Identify the situation before writing a formula.
Surface tension equals force divided by the length along which it acts.
Surface tension is the force per unit length acting along a line on the liquid surface.
Use when — A force is described as acting along a line drawn on a liquid surface.
Common trap — Treating surface tension as a bulk force rather than a force confined to the surface.
Surface tension equals work done divided by the increase in surface area.
Surface tension equals the work done per unit increase in surface area at constant temperature.
Use when — A surface area is increased and the associated work or energy is asked for.
Common trap — Forgetting to double the area for a two-surface film such as a soap film.
Work done equals surface tension times twice the increase in one-face area.
Work done to increase a soap film of given area, counting both surfaces of the film.
Use when — The film has two liquid-air surfaces, such as a soap film stretched on a frame.
Common trap — Using a single-surface area when the film actually has two exposed surfaces.
Excess pressure equals two times surface tension divided by the radius.
Excess pressure inside a spherical liquid drop or a gas bubble inside a liquid, with one liquid surface.
Use when — Exactly one liquid-air interface bounds the sphere.
Common trap — Applying this single-surface relation to a soap bubble in air, which has two surfaces.
Excess pressure equals four times surface tension divided by the radius.
Excess pressure inside a soap bubble in air, accounting for its two liquid-film surfaces.
Use when — The bubble is a thin liquid film with air on both sides, giving two surfaces.
Common trap — Using the single-surface relation for a bubble that actually has two film surfaces.
Height of rise equals two times surface tension times cosine of the angle of contact, divided by density, gravity and radius.
Height risen or depressed by a liquid in a narrow tube of given radius, set by the balance of the meniscus pressure difference and the weight of the raised column.
Use when — The tube radius is small enough that the liquid surface inside forms a near-spherical meniscus.
Common trap — Ignoring the sign carried by the angle of contact, which decides rise versus depression.
Tube radius equals meniscus radius of curvature times cosine of the angle of contact.
Relates a capillary tube's radius to the radius of curvature of the meniscus formed inside it, through the angle of contact.
Use when — The meniscus is treated as a spherical cap inside a narrow tube.
Common trap — Confusing the tube radius with the meniscus radius of curvature when the angle of contact is not zero.
Excess pressure equals surface tension times the sum of the reciprocals of the two principal radii of curvature.
General excess pressure across a curved liquid surface with two principal radii of curvature, of which the spherical drop relation is a special case.
Use when — The liquid surface is not a simple sphere, such as a curved film with two distinct curvatures.
Common trap — Applying the simple 2T/r drop relation to a surface that is not spherical.
Answer: Excess pressure inside the soap bubble is 4T/r, twice the value for a drop of the same radius and surface tension, because the bubble has two liquid-air surfaces.
A liquid drop has a single liquid-air surface, so its excess pressure is 2T/r. A soap bubble is a thin liquid film with air on both the inside and outside, giving two liquid-air surfaces. Each surface contributes an inward pull of T/r type magnitude, so the two surfaces add to give an excess pressure of 4T/r.
The surface count, not the formula alone, is what must be checked first: mistaking a bubble for a drop halves the correct excess pressure.
Answer: The sign of cosine of the angle of contact, positive for water on glass and negative for mercury on glass, is what decides rise versus depression in the capillary relation.
Water wets glass, giving an acute angle of contact and a concave meniscus. In the capillary rise relation, cosine of an acute angle is positive, so the relation predicts a positive height, meaning the water surface rises inside the tube until the raised column's weight balances the pressure difference at the meniscus.
Mercury does not wet glass, giving an obtuse angle of contact and a convex meniscus. Cosine of an obtuse angle is negative, so the same relation predicts a negative height, meaning the mercury surface inside the tube is depressed below the level outside.
Using the single-surface excess pressure relation for a soap bubble
Knowledge gapWhy it happens
A soap bubble in air has two liquid-air surfaces, not one.
How it is corrected
Use 4T/r for a soap bubble in air and 2T/r for a drop or a bubble inside a liquid.
Dropping the sign carried by the angle of contact in capillary rise
Execution errorWhy it happens
Cosine of the angle of contact can be negative for a non-wetting liquid, which changes rise to depression.
How it is corrected
Read the angle of contact first and keep its sign through the calculation.
Computing work done on a soap film using only one face's area
Execution errorWhy it happens
A soap film has two exposed surfaces, so the true increase in surface area is twice the increase in one face.
How it is corrected
Multiply the one-face area change by two before multiplying by surface tension.
Assuming surface tension always decreases with any impurity
Knowledge gapWhy it happens
The direction of change from an impurity depends on the specific solute and liquid and is not fixed in one direction.
How it is corrected
Read the direction of change from the data given in the question rather than from a memorised assumption.
Using the capillary tube's radius as the meniscus radius of curvature directly
Execution errorWhy it happens
The two radii are equal only when the angle of contact is zero; otherwise they are related through cosine of the angle of contact.
How it is corrected
Use r = R cos(theta) to convert between tube radius and meniscus radius of curvature when the angle of contact is not zero.
Bringing viscosity or Stokes' law reasoning into a surface tension question
Decision / selection errorWhy it happens
Surface tension concerns a static liquid surface's energy and curvature; viscosity and Stokes' law concern resistance to relative motion within a moving fluid.
How it is corrected
Keep the two topics separate; viscosity, Stokes' law and terminal velocity are covered on the Fluid Mechanics page.
Not recognising that the force-per-length and energy-per-area descriptions of surface tension are the same quantity
Knowledge gapWhy it happens
Treating them as unrelated quantities can lead to inconsistent units or an extra unnecessary conversion.
How it is corrected
Recall that N/m and J/m^2 are dimensionally identical for surface tension and switch between them as convenient.
FAQ
Straight answers about how Rank Sarthi fits into serious exam preparation.
Surface tension is the property of a liquid surface that makes it behave like a stretched elastic membrane, caused by unbalanced intermolecular attraction on surface molecules compared with bulk molecules.
A soap bubble in air has two liquid-air surfaces while a drop has only one, so the bubble's excess pressure relation carries an extra factor of two.
It tells you whether a liquid wets a given solid surface. An acute angle of contact indicates wetting with a concave meniscus, and an obtuse angle indicates non-wetting with a convex meniscus.
For most liquids surface tension decreases as temperature rises and becomes zero at the critical temperature, but the effect of a specific impurity should be read from the given data rather than assumed.
Mercury does not wet glass, so its angle of contact is obtuse and the capillary rise relation gives a negative height, meaning depression rather than rise.
Evidence boundary: the syllabus mapping is tied to the official current JEE Main and JEE Advanced documents. No chapter weightage, question frequency, or forecast is asserted. Official papers are linked for evidence-safe practice, and any question classified by chapter requires human academic review first.
Contributor requirements for this page
