Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
A raindrop of diameter 4 mm is about to fall on the ground. Calculate the pressure inside the raindrop. [Surface tension of water T = 0.072 N/m, atmospheric pressure = 1.013 x 105 N/m2 ]
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?
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
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).
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?
If a mosquito is dipped into water and released, it is not able to fly till it is dry again. Explain
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?
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 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
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 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.
Solve the previous problem if the lead piece is fastened on the top surface of the block and the block is to float with its upper surface just dipping into water.
Obtain an expression for the capillary rise or fall using the forces method.
A certain number of spherical drops of a liquid of radius R coalesce to form a single drop of radius R and volume V. If T is the surface tension of the liquid, then
Define the angle of contact for a given pair of solid and liquid.
What are the factors affecting the surface tension of a liquid?
Is surface tension a vector?
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]
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)
The surface tension of boiling water is ______.
