HEAT. 685 HEAT. International Congress of Fhysics, vol. i., Paris, 1900.) It should be noted that previous to the experiments of Joule both Carnot and Mayer had made calculations of the mechauical equivalent of heat, using the numerical values found for cer- tain properties of gases. Specific He.t. It is found by experiment that the heat-energy required to raise the temperature of bodies varies greatly with the material of the body, with the external conditions, and slightly with the initial temperature. The number of ca- lories required to raise the temperature of 1 gram of a substance from t° to (<-f- 1)° under given conditions is called the 'specific heat' of that substance at i° and under the specified conditions. Ordinarily, these conditions are those of con- stant atmospheric pressure ; but it is possible to make the condition one of constant volume in the case of gases. (Methods' for the measurement of specific heats are described under Caloruie- TRY. ) The specific heat of a gas at constant pressure is greater than that at constant volume by an amount equivalent to the energy required to expand the gas against the constant pressure, because, as has been stated, no appreciable work is necessary to produce the expansion of the gas itself. The ratio of these two specific heats of a gas is a most important constant for that gas, and may be determined directly by several meth- ods. Its value for hydrogen, oxygen, and nitro- gen is almost exactly 1.4. (See Elasticity.) The specific heat of a substance varies with its temperature. Its value for water at different temperatures is now known quite exactly owing to the recent experiments of Callendar and Barnes. Its value for solids at different tem- peratures is hard to obtain ; and under ordinary conditions the variations are not important. Boron, carbon, silicon, and iron, however, have specific heats, which increase markedly with in- crease of temperature. The specific heat of a substance which can exist in several allotropic forms varies with the modification: thus at ordi- nary temperatures the specific heat of graphite is 0.202, of charcoal is 0.241, of diamond is 0.147. When a substance changes its state from solid to liquid and then to vapor, its specific heat changes too; thus the specific heat of ice is about 0..50, of water it is 1.00. of steam it is 0.48. Owing to this change in the specific heat of a substance when its molecular arrangement is altered, there is a curious property observed in the case of iron. If an iron wire is raised to a 'red heat' in a flame, then removed and allowed to cool, its color disappears, then reappears, and soon disappears again for good. This is called rccalescence. It is due to the fact that as the iron first cools from its red heat it comes to a state when the molecules rearrange themselves owing to some internal condition of instability, and in so doing liberate energy, which is at once manifest by the iron becoming red-hot again, but at a lower temperature than before. It was observed by Dulong and Petit that, if the specific heats of different solids are compared, there is an approximate connection between them and the atomic weights of the solids. In fact, the product of the specific heat of a substance in the solid condition and its atomic weight is ap- proximately the same for all substances, viz. 6.4. This product for any substance is called its 'atomic heat.' because by the definition of 'atomic ■weight' it is proportional to the heat-energy re- quired to raise the tem])erature of one atom one degree. The agreement between the values of the atomic heat for different substances is not very exact, partly no doubt due to the fact that the conditions of temperature under which the spe- cific heats were measured were not such as to make the other conditions of the solids com- parable, e.g. one solid is nearer its melting-pcjint than is another at the same tem])erature. This law of Dulong and Petit has been cxU-nded l)y Woestyn to the idea of 'molecular lieats;" lie thinks it probable that the heat-energy required to raise the temperature of a molecule one de- gree equals the sum of the amounts of energy re- quii'ed to raise the temperature of the individual atoms. This extension of the law is not verified in the case of most compounds. Table of SPECinc Heats SUBSTANCE Specific heat Tempera- ture Water 1.000 0.033 0.092 0.110 0.093 0.032 15°C 20° 60° 60° Zino 50° 60° Specific Heats OP Gases Constant pressure Constant volume Air 0.2374 0.2169 3.4090 0.2438 0.2176 0.1721 side 0.1730 Hvdrogen 2.402 Oxygen Expansion. In general when heat-energy is .added to a body its volume is changed ; and ex- periments prove that an approximate relation connects the change in volume of any substance and its change in temperature. If Va is the volume at 0°, and « is the volume at t", the ex- ternal pressure remaining constant, v — !;« = !'o/3< or i; = i'o (1 -f- /3(), where /3 is approximately a constant for any one substance (with certain marked exceptions) . It is called the coefficient of cubical expansion at constant pressure, referred to 0'. [A more exact relation would be v = I'o {l + ayt + a^t- + ast' + etc. ) .] If the change in length of a linear dimension of the body — e.g. an edge of a cube, if it is in that form — is con- sidered, it will satisfy a similar formula. Let / and la be the final and initial lengths : then J =: Z„ (1 -- at) , where a is called the coefficient of linear expansion. If the body is in the form of a cube, whose edges have the length /„ at 0° and !j, L, I,, respectively at t°, v^ = 'o', r> ^= I J J,. Hence, if I, =1, a + a,t), L==l, a + z t), I, = La+ a,l) v=Vo [1 + (Oi + a^ -f 03) e + (tti 02 + a, 03 + O3 a,) <2 -|- Oj a., O3 (']. But since Oj, a^, a^ are all extremely small in general this may be written v = v^ [1 -f (a, -f- a, +<t3)< ] ; and it follows that Oj + a^ + <«3 = ?■ [f the body is isotropic, o, = o, =03 =| ^; but if the body is crystalline the coeflicients of linear expansion in different directions may be different, and may even be of opposite sign. In this last case it might happen that the contraction in one direction would be so great as to luako /3 nega- tive, i.e. produce a diminution of volume with rise in temperature. The cliange in volume of.
