10.2 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

The angle between the tangent to the liquid surface at the point of contact and the surface inside the liquid is called the angle of contact ( $\theta )$ , as shown in the diagram

$S_{la}$ = Interfacial tension between liquid-air interface

$S_{sl}$ = Interfacial tension between solid -liquid interface

$S_{sa}$ = Interfacial tension between solid-air interface

At the line of contact of contact, the surface forces between the three media must be in equilibrium. Hence

$\cos ?\theta$ = $\frac{S_{sa}-S_{la}}{S_{la}}$

The angle of contact $\theta$ is obtuse, if $S_{sa}<S_{la}$ , as in the case of mercury on glass

This angle is acute if $S_{sl}<S_{la}$ , as in the case of water on glass

Mercury molecules (which mak

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The angle between the tangent to the liquid surface at the point of contact and the surface inside the liquid is called the angle of contact ( $\theta )$ , as shown in the diagram

$S_{la}$ = Interfacial tension between liquid-air interface

$S_{sl}$ = Interfacial tension between solid -liquid interface

$S_{sa}$ = Interfacial tension between solid-air interface

At the line of contact of contact, the surface forces between the three media must be in equilibrium. Hence

$\cos ?\theta$ = $\frac{S_{sa}-S_{la}}{S_{la}}$

The angle of contact $\theta$ is obtuse, if $S_{sa}<S_{la}$ , as in the case of mercury on glass

This angle is acute if $S_{sl}<S_{la}$ , as in the case of water on glass

Mercury molecules (which makes an obtuse angle with glass) have a strong force of attraction between themselves and a weak force of attraction towards solids. Hence, they tend to form drops

Water molecules make acute angles with glass. They have a weak force of attraction between themselves and a strong force of attraction towards solids. Hence, they tend to spread out

Surface tension is the force acting per unit length at the interface between the plane of a liquid and any other surface. This force is independent of the area of the liquid surface. Hence, surface tension is independent of the area of the liquid surface.

Water with detergent dissolved in it has a small angle of contact( $\theta ).$ This is because for a small $\theta ,$ there is a fast capillary rise of the detergent in the cloth. The capillary rise of a liquid is directly proportion to the cosine of the angle $\theta .$ If $\theta$ is small, then cos $\theta$ will be large and then the rise of detergent in the cloth will be faster.

A liquid tend to acquire the minimum surface area because of the presence of surface tension. The surface area of a sphere is the minimum for a given volume. Hence, under no external forces, liquid drops always take spherical shape.

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<p><picture><img src="https://images.shiksha.com/mediadata/images/articles/1728390225phpOufEP3.jpeg" alt="" width="316" height="178"></picture></p><p>The angle between the tangent to the liquid surface at the point of contact and the surface inside the liquid is called the angle of contact (&nbsp;<span title="Click to copy mathml"><math><mi>θ</mi><mo>)</mo></math></span> , as shown in the diagram</p><p><span title="Click to copy mathml"><math><msub><mrow><mrow><mi>S</mi></mrow></mrow><mrow><mrow><mi>l</mi><mi>a</mi></mrow></mrow></msub></math></span>&nbsp;= Interfacial tension between liquid-air interface</p><p><span title="Click to copy mathml"><math><msub><mrow><mrow><mi>S</mi></mrow></mrow><mrow><mrow><mi>s</mi><mi>l</mi></mrow></mrow></msub></math></span>&nbsp;= Interfacial tension between solid -liquid interface</p><p><span title="Click to copy mathml"><math><msub><mrow><mrow><mi>S</mi></mrow></mrow><mrow><mrow><mi>s</mi><mi>a</mi></mrow></mrow></msub></math></span>&nbsp;= Interfacial tension between solid-air interface</p><p>At the line of contact of contact, the surface forces between the three media must be in equilibrium. Hence</p><p><span title="Click to copy mathml"><math><mrow><mrow><mi mathvariant="normal">cos</mi></mrow><mo>?</mo><mrow><mi>θ</mi></mrow></mrow></math></span>&nbsp;=&nbsp;<span title="Click to copy mathml"><math><mfrac><mrow><mrow><msub><mrow><mrow><mi>S</mi></mrow></mrow><mrow><mrow><mi>s</mi><mi>a</mi></mrow></mrow></msub><mo>-</mo><msub><mrow><mrow><mi>S</mi></mrow></mrow><mrow><mrow><mi>l</mi><mi>a</mi></mrow></mrow></msub></mrow></mrow><mrow><mrow><msub><mrow><mrow><mi>S</mi></mrow></mrow><mrow><mrow><mi>l</mi><mi>a</mi></mrow></mrow></msub></mrow></mrow></mfrac></math></span></p><p>The angle of contact&nbsp;<span title="Click to copy mathml"><math><mi>θ</mi></math></span>&nbsp;is obtuse, if&nbsp;<span title="Click to copy mathml"><math><msub><mrow><mrow><mi>S</mi></mrow></mrow><mrow><mrow><mi>s</mi><mi>a</mi></mrow></mrow></msub><mo>&lt;</mo><msub><mrow><mrow><mi>S</mi></mrow></mrow><mrow><mrow><mi>l</mi><mi>a</mi></mrow></mrow></msub></math></span> , as in the case of mercury on glass</p><div><div><picture><source srcset="https://images.shiksha.com/mediadata/images/articles/1728390291phpUZvuuQ_480x360.jpeg" media="(max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/articles/1728390291phpUZvuuQ.jpeg" alt="" width="361" height="144"></picture></div></div><p>This angle is acute if&nbsp;<span title="Click to copy mathml"><math><msub><mrow><mrow><mi>S</mi></mrow></mrow><mrow><mrow><mi>s</mi><mi>l</mi></mrow></mrow></msub><mo>&lt;</mo><msub><mrow><mrow><mi>S</mi></mrow></mrow><mrow><mrow><mi>l</mi><mi>a</mi></mrow></mrow></msub></math></span> , as in the case of water on glass</p><p>Mercury molecules (which makes an obtuse angle with glass) have a strong force of attraction between themselves and a weak force of attraction towards solids. Hence, they tend to form drops</p><p>Water molecules make acute angles with glass. They have a weak force of attraction between themselves and a strong force of attraction towards solids. Hence, they tend to spread out</p><p>Surface tension is the force acting per unit length at the interface between the plane of a liquid and any other surface. This force is independent of the area of the liquid surface. Hence, surface tension is independent of the area of the liquid surface.</p><p>Water with detergent dissolved in it has a small angle of contact(&nbsp;<span title="Click to copy mathml"><math><mi>θ</mi><mo>)</mo><mo>.</mo><mi></mi></math></span>&nbsp;This is because for a small&nbsp;<span title="Click to copy mathml"><math><mi>θ</mi><mo>,</mo><mi></mi></math></span>&nbsp;there is a fast capillary rise of the detergent in the cloth. The capillary rise of a liquid is directly proportion to the cosine of the angle&nbsp;<span title="Click to copy mathml"><math><mi>θ</mi><mo>.</mo><mi></mi></math></span>&nbsp;If&nbsp;<span title="Click to copy mathml"><math><mi>θ</mi></math></span>&nbsp;is small, then cos&nbsp;<span title="Click to copy mathml"><math><mi></mi><mi>θ</mi></math></span>&nbsp;will be large and then the rise of detergent in the cloth will be faster.</p><p>A liquid tend to acquire the minimum surface area because of the presence of surface tension. The surface area of a sphere is the minimum for a given volume. Hence, under no external forces, liquid drops always take spherical shape.</p>

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