the temperature falls from that point down to 0° C., water exhibits the peculiar property of expanding with a decrease in temperature. We learn, therefore, that water has its maximum density at a temperature of 4° C. 167. The cooling of a lake in winter. The preceding paragraph makes it easy to understand the cooling of any large body of water with the approach of winter. The surface layers are first cooled and contract. Hence, being then eavier than the lower layers, they sink and are replaced y the warmer water from beneath. This process of cooling the surface, and sinking, goes on until the whole body of ter has reached a temperature of 4° C. After this condihas been reached, further cooling of the surface layers es them lighter than the water beneath, and they now in on top until they freeze. Thus, before any ice whatcan form on the surface of a lake, the whole mass of 1 to the very bottom must be cooled to 4° C. This y it requires a much longer and more severe period 1 to freeze deep bodies of water than shallow ones. since the circulation described above ceases at actically all of the unfrozen water will be at 4° C. he coldest weather. Only the water which is in iate neighborhood of the ice will be lower than fact is of vital importance in the preservation of EXPANSION OF LIQUIDS AND SOLIDS 164. The expansion of liquids. The expansion of liquids. differs from that of gases in that 1. The coefficients of expansion of liquids are all considerably smaller than those of gases. 2. Different liquids expand at wholly different rates; for example, the coefficient of alcohol between 0° and 10° C. is .0011; of ether it is .0015; of petroleum, .0009; of mercury, .000181. 3. The same liquid often has different coefficients at different temperatures; that is, the expansion is irregular. Thus, if the coefficient of alcohol is obtained between 0° and 60° C., instead of between 0° and 10° C., it is .0013 instead of .0011. The coefficient of mercury, however, is very nearly constant through a wide range of temperature, which indeed might have been inferred from the fact that mercury thermometers agree so well with gas thermometers. 165. Method of measuring the expansion coefficients of liquids. One of the most convenient and common methods of measuring the coefficients of liquids is to place them in bulbs of known volume, provided with capillary necks of known diameter, like that shown in Fig. 149, and then to watch the rise of the liquid in the neck for a given rise in temperature. A certain allowance must be made for the expansion of the bulb, but this can readily be done if the coefficient of expansion of the substance of which the bulb is made is known. t..... FIG. 149. Bulb for investigating expansions of liquids 166. Maximum density of water. When water is treated in the way described in the preceding paragraph, it reaches its lowest position in the stem at 4° C. As the temperature falls from that point down to 0° C., water exhibits the peculiar property of expanding with a decrease in temperature. We learn, therefore, that water has its maximum density at a temperature of 4° C. 167. The cooling of a lake in winter. The preceding paragraph makes it easy to understand the cooling of any large body of water with the approach of winter. The surface layers are first cooled and contract. Hence, being then heavier than the lower layers, they sink and are replaced by the warmer water from beneath. This process of cooling at the surface, and sinking, goes on until the whole body of water has reached a temperature of 4° C. After this condition has been reached, further cooling of the surface layers makes them lighter than the water beneath, and they now remain on top until they freeze. Thus, before any ice whatever can form on the surface of a lake, the whole mass of water to the very bottom must be cooled to 4° C. This is why it requires a much longer and more severe period of cold to freeze deep bodies of water than shallow ones. Further, since the circulation described above ceases at 4° C., practically all of the unfrozen water will be at 4° C. even in the coldest weather. Only the water which is in the immediate neighborhood of the ice will be lower than 4° C. This fact is of vital importance in the preservation of aquatic life. 168. Expansion of solids. The proofs of expansion of solids with an increase in temperature may be seen on every side. Railroad rails are laid with spaces between their ends so that they may expand during the heat of summer without crowding each other out of place. Wagon tires are made smaller than the wheels which they are to fit. They are then heated until they become large enough to be driven on, and in cooling they shrink again and thus grip the wheels with immense force. A common lecture-room demonstration of expansion is the following: Let the ball B, which when cool just slips through the ring R, be heated in a Bunsen flame. It will now be found too large to pass through the ring; but if the ring is heated, or if the ball is again cooled, it will pass through easily (see Fig. 150). R B FIG. 150. Expansion of solids If the expansion of gases and liquids is due to the increase in the average kinetic energy of agitation of their molecules, the foregoing experiments with solids must clearly be given a similar interpretation. In a word, then, the temperature of a given substance, be it solid, liquid, or gas, is determined by the average kinetic energy of agitation of its molecules. 169. Linear coefficients of expansion of solids. It is often more convenient to measure the increase in length of one edge of an expanding solid than to measure its increase in volume. The ratio between the increase in length per degree rise in temperature and the total length is called the linear coefficient of expansion of the solid. Thus, if 7, represent the length of a bar at to, and 1, its length at to, the equation which defines the linear coefficient k is 2 The linear coefficients of a few common substances are given in the following table: APPLICATIONS OF EXPANSION 170. Compensated pendulum. Since a long pendulum vibrates more slowly than a short one, the expansion of the rod which carries the pendulum bob causes an ordinary clock to run too slowly in summer, and its contraction causes it to run too fast in winter. For this reason very accurate clocks are provided with compensated pendulums, which are so constructed that the distance of the bob beneath the point of support is independent of the temperature. This is accomplished by suspending the bob, by means of two sets of rods of different material, in such a way that the expansion of one set raises the bob, while the expansion of the other set lowers it. Such a pendulum is shown in Fig. 151. The expansion of the iron rods b, d, e, and i tends pensated pendulum to lower the bob, while that of the copper FIG. 151. The com rods e tends to raise it. In order to produce complete compensation it is only necessary to make the total lengths of iron and copper rods inversely proportional to the coefficients of expansion of iron and copper. 171. Compensated balance wheel. In the balance wheel of an accurate watch (Fig. 152) another application of the unequal expansion of metals is made. Increase in temperature both increases the radius of the wheel and weakens the elasticity of the spring which controls it. Both of these effects tend to make the watch lose time. This tendency may be counteracted by bringing the mass of the rotating parts in toward FIG. 152. The compensated balance wheel |