Advertisements
Advertisements
Question
Show that the surface tension of a liquid is numerically equal to the surface energy per unit
area.
Advertisements
Solution
a) Let ABCD be an open rectangular frame of wire on which a wire PQ can slide without
friction
b) The frame held in horizontal position is dipped into soap solution and taken out so that
a soap film APQB is formed. Due to surface tension of soap solution, a force ‘F’ will act on the wire PQ which tends to pull it towards AB.
c) Magnitude of force due to surface tension is, F = 2Tl. [∵ T = F/l]
(A factor of 2 appears because soap film has two surfaces which are in contact with
wire.)
d) Let the wire PQ be pulled outwards through a small distance ‘dx’ to the position P'Q',
by applying an external force F′ equal and opposite to F. Work done by this force,
ΔW = F′dx = 2Tldx.
e) But, 2ldx = ΔA = increase in area of two surfaces of film
∴ ΔW = T ΔA
This work done is stored in the form of potential energy (surface energy).
∴ Surface energy, E = TΔA
∴ `E/(ΔA) = T`
Hence, surface tension = surface energy per unit area
f) Thus, surface tension is equal to the mechanical work done per unit surface area of the
liquid, which is also called as surface energy.
APPEARS IN
RELATED QUESTIONS
Explain why Water on a clean glass surface tends to spread out while mercury on the same surface tends to form drops. (Put differently, water wets glass while mercury does not.)
Explain why Surface tension of a liquid is independent of the area of the surface
Fill in the blanks using the word(s) from the list appended with each statement
Surface tension of liquids generally . . . with temperatures (increases / decreases)
Mercury has an angle of contact equal to 140° with soda lime glass. A narrow tube of radius 1.00 mm made of this glass is dipped in a trough containing mercury. By what amount does the mercury dip down in the tube relative to the liquid surface outside? Surface tension of mercury at the temperature of the experiment is 0.465 N m–1. Density of mercury = 13.6 × 103 kg m–3
The contact angle between pure water and pure silver is 90°. If a capillary tube made of silver is dipped at one end in pure water, will the water rise in the capillary?
A uniform vertical tube of circular cross section contains a liquid. The contact angle is 90°. Consider a diameter of the tube lying in the surface of the liquid. The surface to the right of this diameter pulls the surface on the left of it. What keeps the surface on the left in equilibrium?
The force of surface tension acts tangentially to the surface whereas the force due to air pressure acts perpendicularly on the surface. How is then the force due to excess pressure inside a bubble balanced by the force due to the surface tension?
Water near the bed of a deep river is quiet while that near the surface flows. Give reasons.
An ice cube is suspended in vacuum in a gravity free hall. As the ice melts it
When water droplets merge to form a bigger drop
Viscosity is a property of
A liquid is contained in a vertical tube of semicircular cross section. The contact angle is zero. The force of surface tension on the curved part and on the flat part are in ratio
Consider a small surface area of 1 mm2 at the top of a mercury drop of radius 4.0 mm. Find the force exerted on this area (a) by the air above it (b) by the mercury below it and (c) by the mercury surface in contact with it. Atmospheric pressure = 1.0 × 105 Pa and surface tension of mercury = 0.465 N m−1. Neglect the effect of gravity. Assume all numbers to be exact.
The lower end of a capillary tube is immersed in mercury. The level of mercury in the tube is found to be 2 cm below the outer level. If the same tube is immersed in water, up to what height will the water rise in the capillary?
Find the surface energy of water kept in a cylindrical vessel of radius 6.0 cm. Surface tension of water = 0.075 J m−2.
A capillary tube of radius 1 mm is kept vertical with the lower end in water. (a) Find the height of water raised in the capillary. (b) If the length of the capillary tube is half the answer of part , find the angle θ made by the water surface in the capillary with the wall.
The lower end of a capillary tube of radius 1 mm is dipped vertically into mercury. (a) Find the depression of mercury column in the capillary. (b) If the length dipped inside is half the answer of part (a), find the angle made by the mercury surface at the end of the capillary with the vertical. Surface tension of mercury = 0.465 N m−1 and the contact angle of mercury with glass −135 °.
Two large glass plates are placed vertically and parallel to each other inside a tank of water with separation between the plates equal to 1 mm. Find the rise of water in the space between the plates. Surface tension of water = 0.075 Nm−1.
Consider an ice cube of edge 1.0 cm kept in a gravity-free hall. Find the surface area of the water when the ice melts. Neglect the difference in densities of ice and water.
A metal piece of mass 160 g lies in equilibrium inside a glass of water. The piece touches the bottom of the glass at a small number of points. If the density of the metal is 8000 kg/m3, find the normal force exerted by the bottom of the glass on the metal piece.
A ferry boat has internal volume 1 m3 and weight 50 kg.(a) Neglecting the thickness of the wood, find the fraction of the volume of the boat immersed in water.(b) If a leak develops in the bottom and water starts coming in, what fraction of the boat's volume will be filled with water before water starts coming in from the sides?
A cubical block of ice floating in water has to support a metal piece weighing 0.5 kg. Water can be the minimum edge of the block so that it does not sink in water? Specific gravity of ice = 0.9.
Water level is maintained in a cylindrical vessel up to a fixed height H. The vessel is kept on a horizontal plane. At what height above the bottom should a hole be made in the vessel so that the water stream coming out of the hole strikes the horizontal plane at the greatest distance from the vessel.
The surface tension of a liquid at critical temperature is ______
Two soap bubbles have a radius in the ratio of 2:3. Compare the works done in blowing these bubbles.
How does the friction arise between the surfaces of two bodies in relative motion?
Explain elasticity using intermolecular forces.
Define the surface tension of a liquid.
Mention the S.I unit and dimension of surface tension.
Distinguish between cohesive and adhesive forces.
A drop of oil placed on the surface of water spreads out. But a drop of water place on oil contracts to a spherical shape. Why?
Obtain an expression for the excess of pressure inside a
- liquid drop
- liquid bubble
- air bubble
Water rises in a capillary tube of radius r upto a height h. The mass of water in a capillary is m. The mass of water that will rise in a capillary of radius `"r"/4` will be ______.
Two spherical rain drops reach the surface of the earth with terminal velocities having ratio 16 : 9. The ratio of their surface area is ______.
Water rises upto a height h in a capillary tube on the surface of the earth. The value of h will increase, if the experimental setup is kept in [g = acceleration due to gravity]
If the surface tension of a soap solution is 3 × 10-2 N/m then the work done in forming a soap film of 20 cm × 5 cm will be ______.
The excess of pressure, due to surface tension, on a spherical liquid drop of radius 'R' is proportional to ______.
The upward force of 105 dyne due to surface tension is balanced by the force due to the weight of the water column and 'h' is the height of water in the capillary. The inner circumference of the capillary is ______.
(surface tension of water = 7 × 10-2 N/m)
The angle of contact at the interface of water-glass is 0°, Ethylalcohol-glass is 0°, Mercury-glass is 140° and Methyliodide-glass is 30°. A glass capillary is put in a trough containing one of these four liquids. It is observed that the meniscus is convex. The liquid in the trough is ______.
Is surface tension a vector?
Two mercury droplets of radii 0.1 cm. and 0.2 cm. collapse into one single drop. What amount of energy is released? The surface tension of mercury T = 435.5 × 10–3 Nm–1.
This model of the atmosphere works for relatively small distances. Identify the underlying assumption that limits the model.
A liquid flows out drop by drop from a vessel through a vertical tube with an internal diameter of 2 mm, then the total number of drops that flows out during 10 grams of the liquid flow out ______. [Assume that the diameter of the neck of a drop at the moment it breaks away is equal to the internal diameter of tube and surface tension is 0.02 N/m].
A drop of water and a soap bubble have the same radii. Surface tension of soap solution is half of that of water. The ratio of excess pressure inside the drop and bubble is ______.
A coaxial cylinder made of glass is immersed in liquid of surface tension ' S'. Radius of inner and outer surface of cylinder are R1 and R2 respectively. Height till which liquid will rise is (Density of liquid is p):
In a U-tube, the radii of two columns are respectively r1 and r2. When a liquid of density ρ(θ = 0°) is filled in it, a level difference of h is observed on two arms, then the surface tension of the liquid is ______.
Two blocks of masses m and M are connected by means of a metal wire of cross-sectional area A passing over a frictionless fixed pully as shown in the figure. The system is then released. If M = 2m, then the stress produced in the wire is ______.
The surface tension of soap solution is 25 × 10-3 Nm-1. The excess of pressure inside a soap bubble of diameter 1 cm is ______.
A spherical liquid drop of radius R is divided into eight equal droplets. If surface tension is T, then the work done in this process will be ______.
Find the work done when a drop of mercury of radius 2 mm breaks into 8 equal droplets. [Surface tension of mercury = 0.4855 J/m2].
Calculate (i) the pressure due to the weight of the water at a depth of 2.5 m and (ii) the depth below the surface of water at which the pressure due to the weight of the water equals 1.0 atm.
