Advertisements
Advertisements
प्रश्न
The total free surface energy of a liquid drop is `pisqrt2` times the surface tension of the liquid. Calculate the diameter of the drop in S.l. unit.
Advertisements
उत्तर
Given: E = `pi sqrt2` T
To find: Diameter of drop (d)
Formula: E = TΔA
Calculation: ΔA = `4pir^2`
From formula,
E = `4pir^2`T
r = 0.5946 m
∴ d = 2r
= 2(0.5946)
∴ d = 1.1892 m
Diameter of the drop is 1.1892 m.
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.
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.
In which of the following substances, surface tension increases with increase in temperature ?
- Copper
- Molten copper
- Iron
- Molten iron
Explain why Surface tension of a liquid is independent of the area of the surface
A U-shaped wire is dipped in a soap solution and removed. The thin soap film formed between the wire and the light slider supports a weight of 1.5 × 10–2 N (which includes the small weight of the slider). The length of the slider is 30 cm. What is the surface tension of the film?
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
Show that the surface tension of a liquid is numerically equal to the surface energy per unit
area.
State any two characteristics of the angle of contact
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).
If a mosquito is dipped into water and released, it is not able to fly till it is dry again. Explain
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?
Frictional force between solids operates even when they do not move with respect to each other. Do we have viscous force acting between two layers even if there is no relative motion?
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
Water rises in a vertical capillary tube up to a length of 10 cm. If the tube is inclined at 45°, the length of water risen in the tube will be
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.
A barometer is constructed with its tube having radius 1.0 mm. Assume that the surface of mercury in the tube is spherical in shape. If the atmospheric pressure is equal to 76 cm of mercury, what will be the height raised in the barometer tube? The contact angle of mercury with glass = 135° and surface tension of mercury = 0.465 N m−1. Density of mercury = 13600 kg m−3.
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.
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.
A cubical block of wood weighing 200 g has a lead piece fastened underneath. Find the mass of the lead piece which will just allow the block to float in water. Specific gravity of wood is 0.8 and that of lead is 11.3.
A hollow spherical body of inner and outer radii 6 cm and 8 cm respectively floats half-submerged in water. Find the density of the material of the sphere.
A solid sphere of radius 5 cm floats in water. If a maximum load of 0.1 kg can be put on it without wetting the load, find the specific gravity of the material of the sphere.
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.
What will be the shape of the liquid meniscus for the obtuse angle of contact?
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.
Numerical Problem.
A stone weighs 500 N. Calculate the pressure exerted by it if it makes contact with a surface of area 25 cm2.
How is surface tension related to surface energy?
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 ______.
A square frame of each side L is dipped in a soap solution and taken out. The force acting on the film formed is _____.
(T = surface tension of soap solution).
Two small drops of mercury each of radius 'R' coalesce to form a large single drop. The ratio of the total surface energies before and after the change 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 ______.
A large number of liquid drops each of radius 'r' coalesce to form a big drop of radius 'R'. The energy released in the process in converted into kinetic energy of the big drop. The speed of the big drop is ______. (T = surface tension of liquid, p = density of liquid)
Under isothermal conditions, two soap bubbles of radii 'r1' and 'r2' coalesce to form a big drop. The radius of the big drop is ______.
Soap solution is used for cleaning dirty clothes because ______.
The wear and tear in the machine part is due to ______.
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 ______.
The sap in trees, which consists mainly of water in summer, rises in a system of capillaries of radius r = 2.5 × 10–5 m. The surface tension of sap is T = 7.28 × 10–2 Nm–1 and the angle of contact is 0°. Does surface tension alone account for the supply of water to the top of all trees?
Surface tension is exhibited by liquids due to force of attraction between molecules of the liquid. The surface tension decreases with increase in temperature and vanishes at boiling point. Given that the latent heat of vaporisation for water Lv = 540 k cal kg–1, the mechanical equivalent of heat J = 4.2 J cal–1, density of water ρw = 103 kg l–1, Avagadro’s No NA = 6.0 × 1026 k mole–1 and the molecular weight of water MA = 18 kg for 1 k mole.
- Estimate the energy required for one molecule of water to evaporate.
- Show that the inter–molecular distance for water is `d = [M_A/N_A xx 1/ρ_w]^(1/3)` and find its value.
- 1 g of water in the vapor state at 1 atm occupies 1601 cm3. Estimate the intermolecular distance at boiling point, in the vapour state.
- During vaporisation a molecule overcomes a force F, assumed constant, to go from an inter-molecular distance d to d ′. Estimate the value of F.
- Calculate F/d, which is a measure of the surface tension.
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.
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.
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 ______.
A soap film of surface tension 3 × 10-2 formed in a rectangular frame can support a straw as shown in Fig. If g = 10 ms-12, the mass of the straw is ______.
The surface tension of a soap solution is T. The work done in blowing a soap bubble of diameter d to that of a diameter 2d 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 ______.
Work done to blow a bubble of volume V is W. The work done in blowing a bubble of volume 2V will be ______.
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 ______.
Define angle of contact.
