503 cubic inch at 30° 500 cubic inch at 0°; 503-500 500 503-500 500 × 30 = cubic inch increment = cubic inch at 0°; cubic inch increment per cubic inch at 0° = deg. Cent.; Ex. 3. The linear contraction of a casting of tin is inch per foot; find the superficial contraction. Hence 24 is a good approximation for the value arrived at. Ex. 4. The true coefficient of expansion of mercury per degree Centigrade being 1/5550, and its apparent coefficient of expansion per degree Centigrade in glass being 1/6480; find the coefficient of cubical expansion of glass per degree Centigrade. Hence 1/38700 V increment per V original per degree Centigrade. EXERCISE XLIII. 1. The coefficient of the linear contraction of a casting of tin is inch per foot; what is the coefficient of the volume contraction? 2. A lightning-rod made of copper measures 50 feet in length when at the temperature of 0° C.; find its length in summer when heated to the temperature of 27° C. 3. What effect will a rise of temperature of 25 degrees Centigrade have on a measuring chain, supposing that it is correct at 0° C.? What will be the effect of a fall of temperature of the same amount? 4. If a bar of iron has a length of 10 yards at 0° C., what will be its length at 30° C. ? 5. Find how much an iron girder 100 feet long will expand between 32° F. and 68° F. 6. If the expansion of steel is two thirds that of brass under the same change of temperature, what will be the best arrangement of rods of these metals to form a gridiron pendulum? 7. Calculate the cooling effect of a cube of ice 2 feet in the side, taken at 0° C., and reaching 27° C. when its cooling power has been exhausted. 8. A solid weighs 320 grammes in vacuo, 240 grammes in distilled water at 4° C., and 242 grammes in water at 100° C., of which the density is 0.959 gms. per Find the volume of the solid at these two temperatures, and deduce therefrom its mean coefficient of cubical expansion per degree Centigrade. CC. 9. An isotropic solid when immersed in water at 10° C. displaces 600 cubic inches, and at 40° it displaces 604 cubic inches; find its mean rate of linear expansion between 10° and 40°. 0° C. and 100° C. 10. A solid is weighed in a liquid at The volume of the solid at 0° C. is unity, and at 100° C. 1'006. Also the loss of weight by weighing in the liquid is, at 0° C., 1,800 grains, and at 100° C. 1,750 grains. Find the coefficient of dilatation of the liquid. 11. In a vessel of glass of which the coefficient of expansion for the rise of temperature used is 1/7740, the apparent coefficient of expansion of mercury is 1/1296; find the true coefficient of expansion of mercury. 12. Suppose that an English barometer with a brass scale giving true inches at the temperature 62° F., reads 29.5 inches at 45° F.; what is the pressure in true inches of mercury reduced to the density it has at 32° F. ? 13. Find the reading of a thermometer, the bulb of which is plunged in water at the temperature of 100° C., while the stem is exposed to air at the temperature of 10° C. SECTION XLIV.-EXPANSION OF GASES. ART. 195.-Rate of Expansion. When a gas receives an increase of temperature, it may either increase in volume or it may increase in pressure. Hence the rate of expansion due to increase of temperature is specified under the condition that the pressure remains constant ; and the rate of increase of pressure due to increase of temperature under the condition that the volume remains conThe former rate is expressed in the form stant. ap V increment per V at standard temperature =✪ rise. The standard temperature chosen is the freezing point of water. The value a, remains constant whatever the change of temperature from the standard temperature, provided that the gas is not brought near its point of condensation. For air we have, = 1/273 V increment per V at 9° C. deg. Cent. rise. It will be observed that the values for other gases not easily condensed are very approximately the same. ART. 196.-Rate of Increase of Pressure. The rate of increase of pressure under constant volume is expressed in the form a, P increment per P original rise; where P denotes any unit of pressure per square inch. The value of the rate of increase of pressure under constant volume is theoretically the same; thus 1/273 P increment per P at 0° C. = deg. Cent. rise. COEFFICIENT PER DEGREE CENT. OF THE EXPANSION OF A GAS; AND THE COEFFICIENT PER DEGREE CENT. OF THE CHANGE OF PRESSURE of a Gas. ART. 197.-Derived Rates. The rate of expansion for a gas is similar in its nature to rate of simple interest, consequently the derived rates are similar. Since for a gas 1 = V increment per V at 0° C. deg. Cent. rise; 273 therefore for a change to t° C. 1 + t V decrement per V at t° = deg. Cent. fall, t /1+ V dect. per V at t° = deg. Cent. fall, 273 273 i.e., t i.e., 273 (273) 2 + V dect. per V at t° = deg. Cent. fall. Hence the value t/273 is correct only when t/273 is a small fraction. The constant changes its value according to the initial temperature selected. The above rate applies to any change from 0° to a lower temperature, provided the substance is not brought near its point of condensation. It is modified to 1 273 V decrement per V at 0° = deg. Cent. fall. ART. 198.-Change from a Temperature other than the Standard Temperature. To find the volume of a mass of gas originally at t° C. when changed to t2, the pressure being constant. It is done in two steps, by supposing that the gas is reduced from t° to 0° and then raised from 0° to t2°. ART. 199. Absolute Zero of Temperature. be reckoned, not from the freezing point of water, but from a point If temperature |