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
Derive an expression for excess pressure inside a drop of liquid.
Two narrow bores of diameters 3.0 mm and 6.0 mm are joined together to form a U-tube open at both ends. If the U-tube contains water, what is the difference in its levels in the two limbs of the tube? Surface tension of water at the temperature of the experiment is 7.3 × 10–2 N m–1. Take the angle of contact to be zero and density of water to be 1.0 × 103 kg m–3 (g = 9.8 m s–2)
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.
If a mosquito is dipped into water and released, it is not able to fly till it is dry again. Explain
Water near the bed of a deep river is quiet while that near the surface flows. Give reasons.
A heavy mass is attached to a thin wire and is whirled in a vertical circle. The wire is most likely to break
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.
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 °.
Explain the capillary action.
A drop of mercury of radius 0.2 cm is broken into 8 droplets of the same size. Find the work done if the surface tension of mercury is 435.5 dyn/cm.
What will be the shape of the liquid meniscus for the obtuse angle of contact?
Distinguish between cohesive and adhesive forces.
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 ______
The sufrace tension and vapour pressure of water at 20°C is 7.28 × 10–2 Nm–1 and 2.33 × 103 Pa, respectively. What is the radius of the smallest spherical water droplet which can form without evaporating at 20°C?
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 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.
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)
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 ______.
A light metal disc of radius ‘r’ floats on water surface and bends the surface downwards along the perimeter making an angle ‘θ’ with the vertical edge of the disc. If the weight of water displaced by the disc is ‘W’, the weight of the metal disc is ______.
[T = surface tension of water]
