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l M\~2 ans, Thy = K(0,-@-d), , |is.a.constant introduced by Ramsay and Shields (d = 6)., , a constant, varying from 2.12 for associated liquids to 2.22 for, , unassociated ones., , e This shows- that the surface tension. is zero not at the critical, temperature 9. but at a temperature 9 = K(0. — d), a little below, (six degree) the critical temperature. This is depicted by Callendar’s, experiment on water, when he found that the surface tension of, , _water vanishes at 647° absolute, although its critical temperature is, actually 653° absolute., , 4.4 JAEGER’S METHOD FOR DETERMINATION OF, SURFACE TENSION, , e When the column of liquid that rises in a tube dipping vertically into, a liquid is slowly forced down by applying gas pressure, the pressure, steadily increases to a. well marked maximum just before bubble, escape from end of. tube. Jaeger F.M. first employed this, phenomenon to measure surface tension.
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Properties of Matter, , F.Y.B.Sc. Mech. & Prop. of Matter (P-111) (S-1) 4.8, , 2, , The excess pressure inside an air bubble in a liquid is 2T/r, where, T is the surface tension of the liquid and r is the radius of the bubble., This excess pressure (P) is measured by Jaeger's method, which, produces air bubble. Also knowing P and r, the surface tension (T) of, the liquid can be determined easily., , In this method, the apparatus consists of a long thin glass tube AB,, with its lower portion ending in a fine jet of about 0.2 mm to 0.5 mm, in diameter. The tip of the glass tube AB at point B is quite smooth., The glass tube AB is dipped into the experimental liquid about 4 to, 5 cm of its length. The vessel: containing the experimental liquid has, diameter about 8 to 10 cm so that the liquid surface is flat., , Water, , , , , Capillary, , Fig. 4.4 : Jaeger's apparatus, The glass tube is connected to a manometer M and a Woulff’s bottle,, fitted with a dropping funnel F containing water as shown in Fig. 4.4., The liquid used in manometer is other than water which has lower, density so that the difference of level in the two limbs will be large., , Due to capillary action, some liquid rises up into the tube AB. The, shape of its meniscus is nearly hemispherical. Some air is forced into, the tube by dropping water into the Woulff's bottle, which displaces, its own volume of air from it. The liquid column in AB thus slowly, moves down until it reaches to B, when a bubble is formed there. The, radius of curvature of the bubble gradually decreases with increasing, pressure inside it, until it reaches the minimum value, and the bubble
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F.Y.B.Sc. Mech. & Prop. of Matter (P-111) (S-I) 4.9 Properties of Matter, , acquires a hemispherical shape with radius 'r’, equal to that of the, aperture at B. The pressure inside the bubble is maximum indicated, by difference H in two limbs of the manometer as shown in Fig. 4.4., , « The bubble now becomes unstable as it further grows. As its radius, increases, pressure inside it decreases due to surface tension. The, equilibrium between the internal and external pressure is destroyed., Therefore, the bubble gets detached from the tube. The same process, repeats again., , ¢ The accuracy in the result of surfacé tension will be more if the, bubbles form only one at-a time and so slowly that it takes at least, 10 seconds to form one bubble. This can be easily arranged (i) by, reducing the volume of the air space above water in the Woulff's, bottle, so that the pressure in the apparatus falls to a value lower, than that required to blow another and (ii) by properly regulating the, flow of water from the dropping funnel into the Woulff's bottle., , * Now, when just before the bubble breaks away from B, the pressure, inside it is equal to that at C., , The pressure at C will be P; = P + Hpg w+ (4.3), where P is atmospheric pressure and Hpg is the pressure due to the, liquid column H in the manometer and p is its density., When the bubble just break away from B, the pressure on it is equal, to that at level of B in the beaker. /, n P, = P+hdg w. (4.4), where h is the depth the tip B from the surface of liquid in the beaker, and ‘d’ is its density., , Excess pressure ], , Hence, es the bubble] = P1—P2, , (P + Hpg) — (P + hdg), , = g (Hp - hd) .. (4.5), But the excess pressure inside the bubble is 2T/r. ., 27, + = 9 (Hp - hd), (Hp — hd) gr, Us a . (46), , By measuring H, h and r, we can obtain the value of surface tension, of a given liquid.
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F.Y.B.Sc. Mech. & Prop. of Matter (P-111) (S-I)__4.10, , (a), , , , Properties of Matter, , Advantages of Jaeger’s Method :, , The internal radius of the capilllary tube is to be determined at the, aperture (B) at its lower end. Therefore, In Jaeger’s method of, determining surface tension there is no error due to non-uniformity, in the bore of tube., , As a fresh bubble is formed every time, the liquid-air surface is, automatically being renewed, thereby greatly reducing possibility of, error due to contamination of the surface., , The angle of contact between the liquid-glass surfaces is not, required., , The small quantity of liquid is required., , Important Applications of Jaeger’s Method :, , It can be used to study the variation of surface tension with, temperature. ., , By using capillary tube of platinum, surface tension of molten metals, can be determined., , The variation of surface tension of a solution with different, concentration of the solute can be studied., , The surface tensions of different liquids can be easily compared., , The molecular aggregation of the liquid can be studied., , (c) Precautions and sources of error, , 1., , The capillary tube employed in the experiment should be, scrupulously clean as even trace of grease are extremely detriment to, surface tension experiments., , The apparatus should be perfectly air tight. It is therefore, advantageous to have the whole apparatus in one single price,, avoiding use of rubber joints., , The manometer should contain liquid of low density. (For this, purpose, xylol having density = 0.86 gm/c.c is preferable)., , The maximum pressure recorded by manometer should be, independent of formation of bubbles. For this purpose, their, formation should be regulated that successive bubble appear at, interval of nearly ten seconds., , Temperature of water should be invariably recorded and reported, with results. Diameter of orifice should be measured in two, perpendicular directions.
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r.Y.B.Sc. Mech. & Prop. of Matter (P-111) (S-I)_ _4.11 Properties of Matter, , 6., , The chief source of error in the experiment lies in the assumption that, the maximum pressure occurs in the bubble when it is hemispherical, (and that its radius is equal to radius of orifice of capillary tube). Now, this is true when the diameter of orifice is infinitely small, a fact which, cannot be realized in practice., , Secondly the pressure difference H is a small quantity and is, measured by liquid manometer which is not susceptible of yielding, very great accuracy. ,, , The orifice of the tube is, according to theory, should be exactly, circular and it should be held such that it is horizontal. These two, conditions ca ot be realized in practice., , (d) Drawback of Jaeger’s Method :, , There is no absolute certainty that the radius of bubble, when it is, detached from the tube is same as the radius of aperture at B and, it may not be hemispherical. For a greater accuracy in the result, the, following modified relation is used., , r 2r, T= ‘1 Hp a(h 2, , 4.5 APPLICATIONS OF SURFACE TENSION, , 1., , Small insects walk on the free surface of water. Mosquito eggs can, , float on water because of its surface tension. Kerosene is spread on, , the water so that mosquito eggs sin cand breeding stops., The oil and grease spots on cloths cannot be removed by water., When detergent is added in water, the surface tension of water, decreases. As a result of this, wetting power of soap solution in oil or, grease on cloth increases. The oil, grease and dirt properties get, mixed with soap solution easily. Hence the cloths are washed easily, by additions of detergent in the water., , Surface tension of all lubricating oils is kept low so that they spread, over a large area. Also surface tension of paint is made low by adding, liquid like turpentine in it so that paint is spread over large surface., Surface tension impacts and gives early morning dew drops on their, spherical shape because the moisture in the atmosphere condenses, on the beads and leaves due to surface tension., , On the wax cars, the raindrops fall on the surface of the car and they, smoothly slide down keeping the car neat and clean., , Soap is used in toothpaste to enable the paste to quickly spread over, , large area and give a good muscle wash.
