Advertisements
Advertisements
प्रश्न
Calculate the work done in increasing the radius of a soap bubble in air from 1 cm to 2 cm. The surface tension of soap solution is 30 dyne/cm. (Π = 3.142).
Advertisements
उत्तर
Whenever a liquid film is expanded, the work done gets stored as energy in the film. Hence the increase in energy of the film is equal to the work done.
Work done = (increase in the surface ares of bubble) x Surface Tension
Given : r1 = 1 cm, r2 = 2cm, T = 30 dynes/cm
To find : Work (W)
Formula : W = TΔA
Calculation : `A_1 = 4pi r_1^2 = 4pi xx 1^2 = 4pi cm^2`
`A_2 = 4pi r_2^2 = 4pi xx 2^2 = 16 pi cm^2`
`DeltaA = A_2 - A_1 = (16pi - 4pi) = 12 pi cm^2`
Since soap bubble has two surfaces
From formula,
W = 2T x ΔA
= 2 x 30 x 12π
= 2 x 30 x 12 x 3.14
W = `2.26 xx 10^3` erg
`therefore` The work done in increaseing the radius of the soap bubble is 2.26 x 103 erg
APPEARS IN
संबंधित प्रश्न
The energy of the free surface of a liquid drop is 5π times the surface tension of the liquid. Find the diameter of the drop in C.G.S. system.
The surface tension of water at 0°C is 75.5 dyne/cm. Calculate surface tension of water at 25°C.
(α for water = 2.7×10-3/°C)
Define the angle of contact.
Water rises to a height 3.2 cm in a glass capillary tube. Find the height to which the same water will rise in another glass capillary having half area of cross section.
Explain why The angle of contact of mercury with glass is obtuse, while that of water with glass is acute
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.)
Fill in the blanks using the word(s) from the list appended with each statement
Surface tension of liquids generally . . . with temperatures (increases / decreases)
Figure (a) shows a thin liquid film supporting a small weight = 4.5 × 10–2 N. What is the weight supported by a film of the same liquid at the same temperature in Fig. (b) and (c)? Explain your answer physically.
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
Two narrow bores of diameters 3.0 mm and 6.0 mm are joined together to form a U-tube open at both ends. If the U-tube contains water, what is the difference in its levels in the two limbs of the tube? Surface tension of water at the temperature of the experiment is 7.3 × 10–2 N m–1. Take the angle of contact to be zero and density of water to be 1.0 × 103 kg m–3 (g = 9.8 m s–2)
The total energy of free surface of a liquid drop is 2π times the surface tension of the liquid. What is the diameter of the drop? (Assume all terms in SI unit).
In a conical pendulum, a string of length 120 cm is fixed at rigid support and carries a mass
of 150 g at its free end. If the mass is revolved in a horizontal circle of radius 0.2 m around a
vertical axis, calculate tension in the string (g = 9.8 m/s2)
A body weighs 4.0 kg-wt on the surface of the Earth. What will be its weight on the surface of a plant whose mass is `1/8` th of the mass of the Earth and radius half `(1/2)` of that of the Earth?
A big drop of radius R is formed from 1000 droplets of water. The radius of a droplet will be _______
A) 10 R
B) R/10
C) R/100
D) R/1000
The free surface of a liquid resting in an inertial frame is horizontal. Does the normal to the free surface pass through the centre of the earth? Think separately if the liquid is (a) at the equator (b) at a pole (c) somewhere else.
When the size of a soap bubble is increased by pushing more air in it, the surface area increases. Does it mean that the average separation between the surface molecules is increased?
Water near the bed of a deep river is quiet while that near the surface flows. Give reasons.
If water in one flask and castor oil in other are violently shaken and kept on a table, which will come to rest earlier?
A heavy mass is attached to a thin wire and is whirled in a vertical circle. The wire is most likely to break
By a surface of a liquid we mean
Air is pushed into a soap bubble of radius r to double its radius. If the surface tension of the soap solution in S, the work done in the process is
The excess pressure inside a soap bubble is twice the excess pressure inside a second soap bubble. The volume of the first bubble is n times the volume of the second where n is
A 20 cm long capillary tube is dipped in water. The water rises up to 8 cm. If the entire arrangement is put in a freely falling elevator, the length of water column in the capillary tube will be
The properties of a surface are different from those of the bulk liquid because the surface molecules
(a) are smaller than other molecules
(b) acquire charge due to collision from air molecules
(c) find different type of molecules in their range of influence
(d) feel a net force in one direction.
The capillaries shown in figure have inner radii 0.5 mm, 1.0 mm and 1.5 mm respectively. The liquid in the beaker is water. Find the heights of water level in the capillaries. The surface tension of water is 7.5 × 10−2 N m−1.
A drop of mercury of radius 2 mm is split into 8 identical droplets. Find the increase in surface energy. Surface tension of mercury = 0.465 J m−2.
Find the force exerted by the water on a 2 m2 plane surface of a large stone placed at the bottom of a sea 500 m deep. Does the force depend on the orientation of the surface?
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 cube of ice floats partly in water and partly in K.oil (in the following figure). Find the ratio of the volume of ice immersed in water to that in K.oil. Specific gravity of K.oil is 0.8 and that of ice is 0.9.
Why is the surface tension of paints and lubricating oils kept low?
Twenty-seven droplets of water, each of radius 0.1 mm coalesce into a single drop. Find the change in surface energy. Surface tension of water is 0.072 N/m.
A drop of mercury of radius 0.2 cm is broken into 8 droplets of the same size. Find the work done if the surface tension of mercury is 435.5 dyn/cm.
The water droplets are spherical in free fall due to ______
Explain the phenomena of surface tension on the basis of molecular theory.
The property of _______ of a liquid surface enables the water droplets to move upward in plants.
How does surface tension help a plant?
Explain elasticity using intermolecular forces.
Define the angle of contact for a given pair of solid and liquid.
What are the factors affecting the surface tension of a liquid?
A spherical soap bubble A of radius 2 cm is formed inside another bubble B of radius 4 cm. Show that the radius of a single soap bubble which maintains the same pressure difference as inside the smaller and outside the larger soap bubble is lesser than the radius of both soap bubbles A and B.
Why coffee runs up into a sugar lump (a small cube of sugar) when one corner of the sugar lump is held in the liquid?
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 ______.
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 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)
Why is raindrop spherical in nature?
This model of the atmosphere works for relatively small distances. Identify the underlying assumption that limits the model.
A hot air balloon is a sphere of radius 8 m. The air inside is at a temperature of 60°C. How large a mass can the balloon lift when the outside temperature is 20°C? (Assume air is an ideal gas, R = 8.314 J mole–1K–1, 1 atm. = 1.013 × 105 Pa; the membrane tension is 5 Nm–1.)
Eight droplets of water each of radius 0.2 mm coalesce into a single drop. Find the decrease in the surface area.
Two narrow bores of diameter 5.0 mm and 8.0 mm are joined together to form a U-shaped tube open at both ends. If this U-tube contains water, what is the difference in the level of the two limbs, of the tube?
[Take surface tension of water T = 7.3 × 10-2 Nm-1, angle of contact = 0, g = 10 ms-2 and density of water = 1.0 × 103 kgm-3]
We have three identical perfectly black plates. The temperatures of first and third plate is T and 3T. What is the temperature of second plate if system is in equilibrium?
When one end of the capillary is dipped in water, the height of water column is 'h'. The upward force of 105 dyne due to surface tension is balanced by the force due to the weight of water column. The inner circumference of capillary is ______.
(Surface tension of water = 7 × 10-2 N/m)
A liquid drop of density ρ is floating half immersed in a liquid of density d. The diameter of the liquid drop is ______.
(ρ > d, g = acceleration due to gravity, T = surface tension)
In most liquids, with the rise in temperature, the surface tension of a liquid ______.
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 ______.
Define angle of contact.
