# Surface Tension and Capillarity > Surface tension and capillarity for JEE Physics: S = F/l, excess pressure in drops and bubbles, capillary rise and angle of contact effects. - Canonical URL: https://prepelephant.com/topics/jee/physics/surface-tension-and-capillarity - Exam / course: JEE · Subject: Physics - Publisher: PrepElephant (https://prepelephant.com) — Prepared and reviewed by the PrepElephant Academic Review Team - First published: 2026-10-02 - Last updated: 2026-10-02 - How to cite: "Surface Tension and Capillarity", PrepElephant, https://prepelephant.com/topics/jee/physics/surface-tension-and-capillarity ## Direct answer Surface tension S is force per unit length on a liquid surface (also energy per unit area, both numerically equal in N/m), roughly 0.073 N/m for water and 0.48 N/m for mercury at room temperature, and it exists because surface molecules are pulled inward, so the surface contracts like stretched film. Consequences with formulas: excess pressure inside a liquid drop is 2S/r, inside a soap bubble 4S/r (two surfaces), and a soap film on a loop is pierced by 2S per contact line. Capillary rise follows Jurin's law, h = 2 S cos(theta)/(r rho g), positive for water in glass (theta near 0 degrees) and negative — capillary depression — for mercury in glass (theta about 140 degrees). ## What you must remember - **Two equal definitions:** S = F/l = dW/dA; water at 20 degrees is about 0.073 N/m and falls linearly with temperature to zero near the boiling point. - **Excess pressure ladder:** liquid drop 2S/r; soap bubble 4S/r; air bubble in liquid 2S/r; cylindrical jet or tube S/r — the denominator is the radius of curvature, the multiplier counts the surfaces. - **Angle of contact:** water–glass nearly 0 degrees (wetting), mercury–glass about 140 degrees (non-wetting); detergents reduce both S and theta, which is how they clean. - **Capillary rise (Jurin's law):** h = 2 S cos(theta)/(r rho g); halving the tube radius doubles the rise; for water with theta = 0, h r = 2 S/(rho g) is constant along the same liquid. - **Energy of a film:** blowing a soap bubble of radius r needs surface energy 8 pi r^2 S (two surfaces); splitting one drop into n drops conserves volume, shrinks each radius by n^(1/3), and multiplies total surface energy by n^(1/3). - **Needle on water:** floats by surface tension although denser than water — the maximum weight supportable is about 2 S l for a wire of length l before the film breaks. - **Temperature and impurity:** surface tension falls with temperature and with surface-active impurities like detergent; dissolved salts raise it slightly. - **Pattern note:** Main asks the excess-pressure and capillary-rise numericals; Advanced asks energy accounting in drop coalescence and splitting. ## One drop split into eight Take a water drop of radius 3 mm and spray it into 8 identical droplets. Volume conservation fixes the new radius: 8 × (4/3)pi r^3 = (4/3)pi R^3, so r = R/2 = 1.5 mm. Surface energy before is 4 pi R^2 S; after, 8 × 4 pi (R/2)^2 S = 2 × 4 pi R^2 S. The energy has doubled, and the difference is the work the spraying hand supplied. The general law for n droplets: radii shrink by n^(1/3), surface area grows by n^(1/3), and the work done is 4 pi R^2 S (n^(1/3) − 1). The capillary formula rewards the same clean bookkeeping. A tube of radius 0.5 mm dipped in water (S = 0.073, theta ~ 0) rises h = 2 × 0.073/(0.0005 × 1000 × 9.8) = 0.0298 m, about 3 cm; halve the radius and 6 cm appears. ## Where students slip The 2S/r versus 4S/r distinction drops marks every session: a soap bubble has an inner and an outer surface, a liquid drop has one — candidates who count surfaces by intuition instead of by inspection of the film misapply it. Second, cos(theta) is signed: for mercury in glass it is negative and capillary depression follows; quoting a positive rise from the formula without the angle's sign is the error. Third, in energy questions students divide area change by volume change casually; the work done against surface tension is S × change in area, full stop. Finally, radius versus diameter in Jurin's law — the r is the capillary's inner radius, and using the bore diameter halves every answer. ## Frequently asked questions ### Why does a soap bubble have double the excess pressure of a drop? A bubble carries two free surfaces, inner and outer, each contributing 2S/r, giving 4S/r total; a drop exposes only one surface. ### What determines whether a liquid rises or falls in a capillary? The contact angle: h = 2 S cos(theta)/(r rho g) is positive for wetting liquids (water in glass) and negative for non-wetting (mercury in glass, theta about 140 degrees). ### What happens when several small droplets coalesce into one big drop? Total surface area and surface energy decrease, and the energy released slightly warms the drop — radius grows by n^(1/3) of the small radius. ### How does a detergent help in cleaning? It lowers both S and the contact angle, letting water spread over and penetrate the fabric — two effects working jointly. ### Why can a steel needle float on water although steel is denser? The water surface, behaving like a stretched membrane, exerts surface tension along the contact line sufficient to balance the needle's weight until the film is penetrated.