हिंदी

N' Droplets of Equal Size of Radius R Coalesce to Form a Bigger Drop of Radius R. the Energy Liberated is Equal to - Physics

Advertisements
Advertisements

प्रश्न

'n' droplets of equal size of radius r coalesce to form a bigger drop of radius R. The energy liberated is equal to...................

(T =Surface tension of water)

`(a) 4piR^2T[n^(1/3)-1]`

`(b) 4pir^2T[n^(1/3)-1]`

`(c) 4piR^2T[n^(2/3)-1]`

`(d)4 pir^2T[n^(2/3)-1]`

Advertisements

उत्तर

(a) ` 4piR^2T[n^(1/3)-1]`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
2012-2013 (March)

APPEARS IN

वीडियो ट्यूटोरियलVIEW ALL [1]

संबंधित प्रश्न

Derive Laplace’s law for spherical membrane of bubble due to surface tension.


Derive an expression for excess pressure inside a drop of liquid.


The surface tension of water at 0ºc is 75·5 dyne/cm. Find surface tension of water at 25°C. [ α for water = 0·0021/°C ]


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)


Define surface tension and surface energy.


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?


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.


It is said that a liquid rises or is depressed in capillary due to the surface tension. If a liquid neither rises nor depresses in a capillary, can we conclude that the surface tension of the liquid is zero?


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?


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


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 


If more air is pushed in a soap bubble, the pressure in it


The rise of a liquid in a capillary tube depends on

(a) the material
(b) the length
(c) the outer radius
(d) the inner radius of the tube


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.


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.


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 °.


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 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.


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 energy stored in a soap bubble of diameter 6 cm and T = 0.04 N/m is nearly ______.


Explain the capillary action.


Calculate the rise of water inside a clean glass capillary tube of radius 0.1 mm, when immersed in water of surface tension 7 × 10-2 N/m. The angle of contact between water and glass is zero, the density of water = 1000 kg/m3, g = 9.8 m/s2.


The water droplets are spherical in free fall due to ______ 


The surface tension of a liquid at critical temperature is ______ 


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.


Define the angle of contact for a given pair of solid and liquid.


What do you mean by capillarity or capillary action?


What is capillarity?


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.


The surface tension of the two liquids is respectively 20 and 60 dyne cm-1. The liquids drop from the ends of two tubes of the same radius. The ratio of the weights of the two drops is ______


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)


A water drop of radius R' splits into 'n' smaller drops, each of radius 'r'. The work done in the process is ______.

T = surface tension of water


Soap solution is used for cleaning dirty clothes because ______.


The wear and tear in the machine part is due to ______.


What is surface tension? Explain the applications of surface tension.


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). 


This model of the atmosphere works for relatively small distances. Identify the underlying assumption that limits the model.


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.

  1. Estimate the energy required for one molecule of water to evaporate.
  2. Show that the inter–molecular distance for water is `d = [M_A/N_A xx 1/ρ_w]^(1/3)` and find its value.
  3. 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.
  4. 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.
  5. Calculate F/d, which is a measure of the surface tension.

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.


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)


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 drop of water of radius 8 mm breaks into number of droplets each of radius 1 mm. How many droplets will be formed?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×