Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
When two drops form a bigger drop, volume remains conserved.
According to the problem, there is two mercury droplets of different radii collapse into one single drop.
Radius of smaller drop = r1 = 0.1 cm = 10–3 m
Radius of bigger drop = r2 = 0.2 cm = 2 × 10–3 m
Surface tension (T) = 435.5 × 10–3 N/m
Let V1 and V2 be the volumes of these two mercury droplets and the volume of big drops formed by collapsing is V.
The volume of a big drop = Volume of small droplets
`V = V_1 + V_2`
`4/3 πR^3 = 4/3 πr_1^3 + 4/3 πr_2^3`
or `R^3 = r_1^3 + r_2^3`
= (0.1)3 + (0.2)3
= 0.001 + 0.008
= 0.009
or R = 0.21 cm = 2 × 10–3 m
∴ Decrease in surface area,
ΔA = `4πR^2 - (4πr_1^2 + 4πr_2^2)`
= `4π[R^2 - (r_1^2 + r_2^2)]`
Energy released,
`E = T xx ΔA`
= `T xx 4π[R^2 - (r_1^2 + r_2^2)]`
= `435.5 xx 10^-3 xx 4 xx 3.14[(2.1 xx 10^-3)^2 - (1 xx 10^-6 + 4 xx 10^-6)]`
= `435.5 xx 4 xx 3.14[4.41 - 5] xx 10^-6 xx 10^-3`
= – 32.23 × 10–7 ......(Negative sign shows absorption)
Therefore, 3.22 × K–6 J energy will be absorbed. So, the surface area of the water decreases means the surface area of bigger drop is less than the sum of surface area of two smaller drops.
APPEARS IN
संबंधित प्रश्न
Angle of contact for the pair of pure water with clean glass is _______.
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 Surface tension of a liquid is independent of the area of the surface
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
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 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 a glass capillary tube is dipped at one end in water, water rises in the tube. The gravitational potential energy is thus increased. Is it a violation of conservation of energy?
If a mosquito is dipped into water and released, it is not able to fly till it is dry again. Explain
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?
Distinguish between cohesive and adhesive forces.
What are the factors affecting the surface tension of a liquid?
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?
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?
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
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 ______.
The excess pressure inside a liquid drop is 500 Nm-2. If the radius of the drop is 2 mm, the surface tension of the liquid is x × 10-3 Nm-1. The value of x is ______.
Define angle of contact.
