Mechanical Properties of Fluids
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Question : 2
Total: 31
Explain why
(a) The angle of contact of mercury with glass is obtuse, while that of water with glass is acute.
(b) Water on a clean glass surface tends to spread out while mercury on the same surface tends to form drops. (Put differently, water wets glass while mercury does not.)
(c) Surface tension of a liquid is independent of the area of the surface
(d) Water with detergent dissolved in it should have small angles of contact.
(e) A drop of liquid under no external forces is always spherical in shape.
(a) The angle of contact of mercury with glass is obtuse, while that of water with glass is acute.
(b) Water on a clean glass surface tends to spread out while mercury on the same surface tends to form drops. (Put differently, water wets glass while mercury does not.)
(c) Surface tension of a liquid is independent of the area of the surface
(d) Water with detergent dissolved in it should have small angles of contact.
(e) A drop of liquid under no external forces is always spherical in shape.
Solution:
(a) When a small quantity of liquid is poured on solid, threeinterfaces namely liquid-air, solid-air and solid-liquid are formed. Thesurface tensions corresponding to these three interfaces i.e. T L A , T S A T S L
cos θ =
. . . ( i )
In case of mercury-glass,T S A < T S L , T S A < T S L ,
(b) For equilibrium of a liquid drop on the surface of a solid, theequation
T S A = T S L + T L A cos θ . . . ( i )
must be satisfied. For mercury-glass, angle of contact is obtuse. In order to achieve this obtuse value of angle of contact, the mercury tends to form a drop.
But in case of water-glass, the angle of contact is acute, so equation (i) is not satisfied. In order to achieve this acute value of angle of contact, the water tends to spread.
(c) Surface tension of liquid is defined as the force acting per unit length on either side of an imaginary line drawn tangentially on the surface of the liquid at rest. Since this force is independent of the area of the liquid surface, therefore surface tension is also independent of the area of the liquid surface.
(d) We know that the cloth has narrow spaces in the form of fine capillaries. The rise of liquid in a capillary tube is given by
h =
i.e.h ∝ cos θ
(e) In the absence of external forces, only force acting on the liquid drop is due to surface tension. A drop of liquid tends to acquire minimum surface area due to the property of surface tension. Since for a given volume of liquid, surface area is minimum for a sphere, so the liquid drop will always assume a spherical shape.
In case of mercury-glass,
(b) For equilibrium of a liquid drop on the surface of a solid, theequation
must be satisfied. For mercury-glass, angle of contact is obtuse. In order to achieve this obtuse value of angle of contact, the mercury tends to form a drop.
But in case of water-glass, the angle of contact is acute, so equation (i) is not satisfied. In order to achieve this acute value of angle of contact, the water tends to spread.
(c) Surface tension of liquid is defined as the force acting per unit length on either side of an imaginary line drawn tangentially on the surface of the liquid at rest. Since this force is independent of the area of the liquid surface, therefore surface tension is also independent of the area of the liquid surface.
(d) We know that the cloth has narrow spaces in the form of fine capillaries. The rise of liquid in a capillary tube is given by
i.e.
(e) In the absence of external forces, only force acting on the liquid drop is due to surface tension. A drop of liquid tends to acquire minimum surface area due to the property of surface tension. Since for a given volume of liquid, surface area is minimum for a sphere, so the liquid drop will always assume a spherical shape.
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