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 ť° C. = 273 t i.e., t 2 i.e., 273 273/1+273 V dect. per V at t=deg. Cent. fall, 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 V decrement per V at 0° = deg. Cent. fall. 273 ART. 198.-Change from a Temperature other than the Standard Temperature. To find the volume of a mass of gas originally at t1° 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 t1⁄2o. ART. 199.-Absolute Zero of Temperature. be reckoned, not from the freezing point of water, but from a point If temperature 273 degrees Centigrade lower, then the volume of a constant mass of gas will always be proportional to its temperature, provided that the pressure is maintained constant throughout. Hence the connection will be expressed by m V volume = ✪ temperature. The temperature 273 degrees Centigrade below the freezing point of water is called the absolute zero of temperature. It means the temperature at which the pressure or the volume of a mass of gas would vanish, on the supposition that the same rate of expansion held throughout which holds for the gaseous state. EXAMPLES. Ex. 1. 500 cubic centimetres of oxygen gas are measured when the temperature is 20° C., and the temperature is then raised to 40° C., the pressure meanwhile remaining constant. What is the volume of the oxygen at the latter temperature? The coefficient of the expansion of oxygen per degree Centigrade is 500 cc. at 20°, 1 1 Ex. 2. Find the mass of 1,000 cubic centimetres of dry air at SO° C. and the pressure of 25 cm. of mercury. 1,000 cubic centi metres of dry air at 0° C. and 76 cm. pressure have a mass of 1.293 grammes. By Art. 134, 1.293 gm. per 1000 cc. at 0° = 76 cm. pressure, 1. A given mass of air occupies a volume of 600 cubic inches at the temperature of 20° C.; find the volume which the air will occupy at 100° C., supposing the pressure to remain constant. 2. A mass of gas occupying a volume of 273 cubic inches at 0° C. is raised in temperature to 150° C. If it be allowed to expand under constant pressure during the process, what will be its new volume? 3. One hundred cubic centimetres of air at 0° C. are heated to 300° C. under constant pressure. What will be the volume of the air at the higher tem perature? 4. A thousand cubic inches of air at the temperature of 30° C. are cooled down to zero, and at the same time the external pressure upon the air is doubled. What is its volume reduced to? 5. Find the temperature to which 500 cubic centimetres of air, measured at 15° C. must be raised in order that the volume of the air may become 700 cubic centimetres, no change of pressure taking place meanwhile. 6. Twenty litres of air are taken at 16° C. and 74 cm. pressure; find the volume of the air at 0° C. and 76 cm. pressure. 7. One thousand cubic inches of gas are taken when the barometer stands at 30.5 inches, and the temperature is 16° C. Find the volume of this gas when the pressure is 29.5 inches and the temperature 12°. 8. Find the absolute zero on the Fahrenheit and on the Réaumur scale. 9. A substance, of the approximate specific gravity 3.2, weighs 180 grammes in dry air of 730 reduced mm. pressure and temperature of 16° C. Also the approximate specific gravity of the weights against which it is weighed is 8.5. Find the real weight of the substance, assuming that the weight of one litre of dry air at 0° C. and 760 reduced millimetres pressure is 1.293187 grammes. SECTION XLV.-THERMAL CONDUCTIVITY. ART. 200.-Conductivity. By the thermal conductivity of a substance is meant the rate connecting the current of heat with the gradient of temperature, when there is a steady flow of heat through the substance. It is expressed in the form H per T per S cross-section = per L normal. By "normal" is meant unit of length along the line of flow, and "per L normal" expresses what is called the gradient of temperature, after the analogy of gradient of gravity (Art. 72). The reciprocal idea is thermal resistance; it is expressed by 1/k per L normal = H per T per S cross-section. When the unit of heat is a dynamical unit, we have conductivity expressed in terms of For example, by W per T per S= per L. erg per sec. per sq. cm. =deg. Cent. per cm.; or, which is the same thing, by erg per sec. per sq. cm. per (deg. Cent. per cm.). for example, deg. Cent. per cm. A value, expressed in terms of this kind of unit, is independent of the magnitude of ; for enters to the same power in the two members of the equivalence. When the units are allowed to cancel one another as much as possible, there remains M/TL, which expresses the dimensions of the unit. ART. 201.-Thermometric Conductivity. Suppose that the conductivity of a substance is k M of water by → per T per S=→ per L, and that the density of water is P M =V; |