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
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 ]
Define the angle of contact.
The contact angle between water and glass is 0°. When water is poured in a glass to the maximum of its capacity, the water surface is convex upward. The angle of contact in such a situation is more than 90°. Explain.
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 capillaries shown in figure have inner radii 0.5 mm, 1.0 mm and 1.5 mm respectively. The liquid in the beaker is water. Find the heights of water level in the capillaries. The surface tension of water is 7.5 × 10−2 N m−1.
Two large glass plates are placed vertically and parallel to each other inside a tank of water with separation between the plates equal to 1 mm. Find the rise of water in the space between the plates. Surface tension of water = 0.075 Nm−1.
Why is the surface tension of paints and lubricating oils kept low?
How much amount of work is done in forming a soap bubble of radius r?
Water rises to a height of 20 mm in a capillary tube. If the radius made 1/3rd of its previous value, to what height will the water now rise in the tube?
Explain the phenomena of surface tension on the basis of molecular theory.
Mention the S.I unit and dimension of surface tension.
Distinguish between cohesive and adhesive forces.
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?
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 ____________.
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
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?
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.)
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 ______.
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)
