Advertisements
Advertisements
प्रश्न
Derive an expression for excess pressure inside a drop of liquid.
Advertisements
उत्तर
Consider a spherical drop as shown in the figure. Let pi be the pressure inside the drop and p0 be the pressure out side it. As the drop is spherical in shape, the pressure, pi, inside the drop is greater than p0, the pressure outside. Therefore, the excess pressure inside the drop is pi - p0.
Let the radius of the drop increase from r to r + ∆r, where ∆r is very small, so that the pressure inside the drop remains almost constant.
Let the initial surface area of the drop be A1 = 4πr2 , and the final surface area of the drop be A2 = 4π (r+∆r)2.
∴ A2 = 4π(r2 + 2r∆r + ∆r2)
∴ A2 = 4πr2 + 8πr∆r + 4π∆r2 (As ∆r is very small, ∆r2 can be neglected)
∴ A2 = 4πr2 + 8πr∆r
Thus, increase in the surface area of the drop is
`dA = A_2 – A_1 = 8πrDeltar`
Work done in increasing the surface area by `dA` is stored as excess surface energy.
`therefore dW = TdA= T (8πrDeltar)` ... (1)
This work done is also equal to the product of the force F which causes increase in the area of the drop and the displacement ∆r which is the increase in the radius of the bubble.
`therefore dW = F∆r` ... (2)
The excess force is given by,
(Excess pressure) ×(Surface area)
∴ F = (pi – p0) 4πr2 ... (3)
Equating Eq. (1), and Eq. (2), we get,
`T(8πrDeltar) = FDeltar`
`therefore T(8πrDeltar) = (p_i – p_0) 4πr^2Deltar` ... (using Eq. (3))
`therefore (p_i – p_0)=(2T)/r`
This equation gives the excess pressure inside a drop of liquid.
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.
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.)
Explain why Water with detergent dissolved in it should have small angles of contact.
Explain why A drop of liquid under no external forces is always spherical in shape
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.
Show that the surface tension of a liquid is numerically equal to the surface energy per unit
area.
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).
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?
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?
By a surface of a liquid we mean
When water droplets merge to form a bigger drop
Viscosity is a property of
The contact angle between a solid and a liquid is a property of
(a) the material of the solid
(b) the material of the liquid
(c) the shape of the solid
(d) the mass of the solid
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
A 5.0 cm long straight piece of thread is kept on the surface of water. Find the force with which the surface on one side of the thread pulls it. Surface tension of water = 0.076 N m−1.
Find the excess pressure inside (a) a drop of mercury of radius 2 mm (b) a soap bubble of radius 4 mm and (c) an air bubble of radius 4 mm formed inside a tank of water. Surface tension of mercury, soap solution and water are 0.465 N m−1, 0.03 N m−1 and 0.076 N m−1 respectively.
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 capillary tube of radius 0.50 mm is dipped vertically in a pot of water. Find the difference between the pressure of the water in the tube 5.0 cm below the surface and the atmospheric pressure. Surface tension of water = 0.075 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.
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.
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.
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 cubical box is to be constructed with iron sheets 1 mm in thickness. What can be the minimum value of the external edge so that the cube does not sink in water? Density of iron = 8000 kg/m3 and density of water = 1000 kg/m3.
A cubical metal block of edge 12 cm floats in mercury with one fifth of the height inside the mercury. Water in it. Find the height of the water column to be poured.
Specific gravity of mercury = 13.6.
Insect moves over the surface of water because of ______.
The surface tension of a liquid at critical temperature is ______
Define surface tension.
Obtain an expression for the capillary rise or fall using the forces method.
A u-tube is made up of capillaries of bore 1 mm and 2 mm respectively. The tube is held vertically and partially filled with a liquid of surface tension 49 dyne/cm and zero angles of contact. Calculate the density of the liquid, if the difference in the levels of the meniscus is 1.25 cm. take g = 980 cm/s2
The property of _______ of a liquid surface enables the water droplets to move upward in plants.
How does the friction arise between the surfaces of two bodies in relative motion?
The wettability of a surface by a liquid depends primarily on
Define the angle of contact for a given pair of solid and liquid.
Obtain an expression for the surface tension of a liquid by the capillary rise method.
A capillary of diameter d mm is dipped in water such that the water rises to a height of 30 mm. If the radius of the capillary is made `(2/3)` of its previous value, then compute the height up to which water will rise in the new capillary?
The wear and tear in the machine part is due to ______.
The length of a needle floating on water is 2 cm. The additional force due to surface tension required to pull the needle out of water will be (S.T. of water = 7.0 × 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?
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.
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?
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):
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)
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].
The surface tension of boiling water is ______.
