covered by a soap film (Fig. 94). What force should be applied to the movable side to counterbalance it? What work will be done if this side of the frame is moved a distance S = 2 cm? What will be the source of this work when the surface of the film is reduced and into what kind of energy will the work be transformed? The length of the movable side is l = 6 cm. The surface tension of the soap film is on = 40 dyn/cm. r t * 7* ll (l/' ’ · ‘! V mv . Fig. 94 Fig. 95 279. A light open rigid paper frame as shown in Fig. 95 floats on the surface of water. What will happen to the frame if some soap solution is dropped inside it? What force will act on the frame and in what direction will it act? 280. When some useless work is done it is commonly said that it is the same as carrying water in a sieve. When can water really be carried in a sieve without it seeping through? What is the maximum height of the water layer that can be carried in a sieve if the diameter of the mesh is d = 1 mm? Can the water poured into a sieve be drained over its edge? The surface tension of water is ot = 70 dyn/cm. 281. Part of a capillary is lowered into a wetting agent. Can the loss of weight of the capillary be calculated by Archimedes’ law? What will the answer be in the case of a non-wetting agent? 282. A capillary of radius r is lowered into a wetting agent with surface tension on and density d.
76 r·no1aLEMs Determine the height ho to which the liquid will rise in the capillary. Calculate the work done by surface tension and the potential energy acquired by the liquid in the capillary and compare the two. Explain the difference in the results obtained. 283. In order to remove paraffine and other fatty spots from fabric they are usually ironed hot through paper. Why does paraffine or fat soak into the paper in this case and not spread over the fabric? l Should the paper used for ironing be I sized or not? _g___* M 284. In a device designed by Aca- _,; demician Rebinder the surface ten- sion is determined from the pressure __ ` difference required to form a bubble Fig, 96 of air at the end of a capillary im- mersed in the liquid being investiga- ted (Fig. 96). Calculate the surface tension if the radius of the capillary is r = 1 mm and the difference in the pressures during bubble formation is AP = 14 mm of water column. The end of the capillary is near the surface of the liquid. 285. The internal radius of one limb of a capillary U—tube is ri = 1 mm and the internal radius of the second limb is rz = 2 mm. The tube is filled with some mercury, and one of the limbs is connected to a vacuum pump. What will be the difference in air pressure when the mercury levels in both limbs are at the same height? Which limb of the tube should be connected to the pump? The surface tension of mercury is 480 dyn/cm. 286. A long capillary tube of radius r = 1 mm open at both ends is filled with water and placed vertically. What will be the height of the column of water left in the capillary? The thickness of the capillary walls is negligible. 287. A capillary tube sealed at the top has an internal radius of r = 0.05 cm. The tube is placed vertically in water, open end first. _ What should the length of such a tube be for the water IH it to rise in these conditions to a height h = 1 cm? The Pressure of the air is P0 = 1 atm. The surface tension of Water is oc = 70 dyn/cm.
CHAPTER 11. HEAT AND MOLECULAR PHYSICS 77 17. Humidity of Air 288. A test—tube of height h is filled to the top with water and its open end is lowered into a glass of water. At what temperature will the level of water move away from the bottom of the test—tube? What will occur in the test-tube if the water is further heated to 100°C? Disregard the action of surface tension. 289. The temperature of the air is ti = 20°C and the dew point tz = 8°C. Find the absolute and relative humidity of the air if the elasticity of the saturated vapour pressure 290. In what conditions can the relative humidity dimi- nish when the absolute humidity of the atmospheric air increases? 291. Two vessels contain air saturated with vapour- one at a temperature of 20°C and the `other at a temperature of 10°C. What amount of dew will be deposited when these two masses of air are mixed if the volumes of the vessels are the same and equal to 1 m3? Assume that within the chosen range the saturated vapour pressure is proportional to the temperature and equal to 9 mm Hg at 10°C and 17 mm Hg at 20°C. Disregard heat losses due to the heat exchange with the walls of the vessel during mixing. 292. A vessel contains air at a temperature of 10°C and humidity of 60 per cent. What will be the relative humidity of this air if it is heated to 100°C and its volume is simultaneously decreased to one third? The absolute humidity corresponding to the saturated vapours at 10°C is 9.43 g/m3. 293. What amount of dew is deposited when a certain volume of air is reduced to one quarter if the initial volume of the air is 1 m3, the temperature 20°C and the humidity 50 per cent? The temperature is constant throughout.
Chapter III ELECTRICITY 18. Coulomb’s Law When studying the fundamentals of electrostatics it is especially important to master hrst Coulomb’s law for calculating the forces produced by a system of electric charges and, particularly, to understand clearly how the principle of independent action of electric charges can be used to solve problems. The problems in this section and their solutions are pre- sented so as to indicate the sequence in which this principle can best be applied, especially when solving the problems in Secs 19, 20 and 21. At the same time these problems allow the reader to revise the methods commonly used for finding the equilibrium of separate bodies and systems. In solving the problems on calculation of electric charges, pay attention to the stability of the equilibrium of charges (for example, if the equilibrium of the charge q in Problem 299 is stable with respect to the movement along a straight line connecting all the three charges it will be unstable with respect to motion in all the other directions). This is a particular case of the general theorem which states that it is impossible to attain a stable equi- librium in a system of free electric charges. 294. How should Coulomb’s law be written in order to obtain the force in kilograms if the charges are in cou- lombs and the distances in metres? 295. Determine the force of electrostatic interaction between the electron and the nucleus in a hydrogen atom. The mean distance of the electron from the nucleus of the atom is 1 >< 10*8 cm and the charge of the electron is e == = 4.8 X 10"1° cgs electrostatic units.
CHAPTER III. ELECTRICITY 79