Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Given:
Edge of the ice cube (a) = 1.0 cm
The water that is formed due to the melting of ice acquires a spherical surface.
In the absence of gravity, let the radius of the spherical surface be r.
Volume of ice cube = volume of spherical surface of water
\[\Rightarrow a^3 = \frac{4}{3}\pi r^3 \]
\[ \Rightarrow r = \left[ \frac{3 a^3}{4\pi} \right]^{1/3}\]
Surface area of spherical water surface = 4πr2
\[= 4\pi \left[ \frac{3 a^3}{4\pi} \right]^{2/3} \]
\[ = \left( 36\pi \right)^{1/3} {\text{ cm }}^2\]
APPEARS IN
संबंधित प्रश्न
Angle of contact for the pair of pure water with clean glass is _______.
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 ]
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.
An ice cube is suspended in vacuum in a gravity free hall. As the ice melts it
The excess pressure inside a soap bubble is twice the excess pressure inside a second soap bubble. The volume of the first bubble is n times the volume of the second where n is
Find the excess pressure inside (a) a drop of mercury of radius 2 mm (b) a soap bubble of radius 4 mm and (c) an air bubble of radius 4 mm formed inside a tank of water. Surface tension of mercury, soap solution and water are 0.465 N m−1, 0.03 N m−1 and 0.076 N m−1 respectively.
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.
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.
A cubical block of wood weighing 200 g has a lead piece fastened underneath. Find the mass of the lead piece which will just allow the block to float in water. Specific gravity of wood is 0.8 and that of lead is 11.3.
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.
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.
Twenty-seven droplets of water, each of radius 0.1 mm coalesce into a single drop. Find the change in surface energy. Surface tension of water is 0.072 N/m.
A u-tube is made up of capillaries of bore 1 mm and 2 mm respectively. The tube is held vertically and partially filled with a liquid of surface tension 49 dyne/cm and zero angles of contact. Calculate the density of the liquid, if the difference in the levels of the meniscus is 1.25 cm. take g = 980 cm/s2
Mention the S.I unit and dimension of surface tension.
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.
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?
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 ______.
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 drop of water of radius 8 mm breaks into number of droplets each of radius 1 mm. How many droplets will be formed?
