78 CHAPTER IX. HEAT. 97. THE unit of heat is usually defined as the quantity of heat required to raise, by one degree, the temperature of unit mass of water, initially at a certain standard temperature. The standard temperature usually employed is 。° C.; but this is liable to the objection that ice may be present in water at this temperature. Hence 4° C. has been proposed as the standard temperature; and another proposition is to employ as the unit of heat one hundredth part of the heat required to raise the unit mass of water from o° to 100° C. 98. According to Regnault (Mém. Acad. Sciences,' xxi. p. 729) the quantity of heat required to raise a given mass of water from o° to t° C. is proportional to (1) t + ·00002 ť2 + 0000003 13. The mean thermal capacity of a body between two stated temperatures is the quantity of heat required to raise it from the lower of these temperatures to the higher, divided by the difference of the temperatures. The mean thermal capacity of a given mass of water between o° C. and is therefore proportional to I + 00002 t + *0000003 12. (2) The thermal capacity of a body at a stated temperature is the limiting value of the mean thermal capacity as the range is indefinitely diminished. Hence the thermal. capacity of a given mass of water at t° is proportional to the differential coefficient of (1), that is to 1 + ·00004 t + ·0000009 t2. (3) Hence the thermal capacities at o° and 4° are as I to 1000174 nearly; and the thermal capacity at o° is to the mean thermal capacity between o° and 100° as I to 1'005. 99. If we agree to adopt the capacity of unit mass of water at a stated temperature as the unit of capacity, the unit of heat must be defined as ʼn times the quantity of heat required to raise unit mass of water from this initial temperature through of a degree when is inde finitely great. I Supposing the standard temperature and the length of the degree of temperature to be fixed, the units both of heat and of thermal capacity vary directly as the unit of mass. In what follows, we adopt as the unit of heat (except where the contrary is stated) the heat required to raise a gramme of pure water through 1° C. at a temperature intermediate between o° and 4°. This specification is sufficiently precise for the statement of any thermal measurements hitherto made. 100. The thermal capacity of unit mass of a substance at any temperature is called the specific heat of the substance at that temperature. The following determinations of specific heat by Dulong and Petit agree very well with later determinations by Regnault and other experimenters, except in the case of 101. Specific heat is of zero dimensions in length, mass, and time. It is in fact the ratio increment of heat in the substance increment of heat in water for a given increment of temperature, the comparison being between equal masses of the substance at the actual temperature and of water at the standard temperature. The numerical value of a given concrete specific heat merely depends upon the standard temperature at which the specific heat of water is called unity. 102. The thermal capacity of unit volume of a substance is another important element: we shall denote it by c. Let s denote the specific heat, and d the density of the substance; then is the thermal capacity of d units of mass, and therefore c=sd. The dimensions of c in length, mass, and time are the same as those of d, namely M Its numerical value will not be altered by any L3 change in the units of length, mass, and time which. leaves the value of the density of water unchanged. In the C.G.S. system, since the density of water between o° and 4° is very approximately unity, the thermal capacity of unit volume of a substance is the value of the ratio increment of heat in the substance increment of heat in water for a given increment of temperature, when the comparison is between equal volumes. 103. The following table (from Miller's Chemical Physics,' p. 313, fourth edition) exhibits the specific heats of most of the elementary bodies, also their atomic weights, and the product of the two :— |