HEAT. OSi HEAT. iron or nitrogen gas initially at a certain den- sity: under two thermal conditinns, assuminc no other changes in external conditions and particu- larly no change in the pressure on the hody. Let V be the volume of the selected body under the thermal condition for which a numerical value is desired, e.g. a vessel of water, the air of a room. Let it be agreed to take n 'degrees' or steps between the two standard thermal states, I'l — V-i then — ■ is the change in volume corre- spending to one degree ; and the number of degrees corresponding to the change in volume v—i is Therefore, if it is agreed to give the number <, to the first thermal state, the proper number for the temperature of the state to which the volume j; corresponds is « = , , + „!=!!, In this method for giving a numerical value to the temperature the following steps are arbi- trary : ( 1 ) Choice of property of body, which varies with the temiierature. (2) Choice of body to serve as 'thermometric substance.' (.3) Choice of two standard thermal states. (4) Choice of number of degrees between the tem- peratures of these states. (5) Choice of number for first state. There are, consequently, an in- definite number of methods for giving numerical values to temperature. (See Thermometry.) The scientific world has agreed to use numbers depending upon the change in voKune or pressure of hydrogen gas initially at a pressure of 100 centimeters of mercury, the standard thermal states being those of melting ice and vapor rising from boiling water under normal atmospheric pressvire, the number of degrees between the temperatures of these states being taken as 100, and the temperature of melting ice being taken as 0. (Therefore the temperature of the other standard state is 100,) Then, in the above for- mula, the numerical value of t becomes t — 100 '^" , - 1 U I r ■ u This is, then, the temperature on a constant pressure hydrogen thermometer. Centigrade scale, [If change in pressure of a gas kept at constant volume is the property measured, the tempera- ture is t = 100 P-P" , Pi Pa where Po, Piw, P are the pressures of the gas at 0°, 100°, t° . E.xperiments show that using hy- drogen the temperature defined this way has the same numerical value as that defined by the change in volume at constant pressure.] It is seen, then, that in order to give a numeri- cal value to a thermal state, e.g. to that of water in a vessel, three measurements are necessary, those of the volume of the hydrogen when the bulb containing it is immersed in melting ice (tv), in vapor rising from boiling water (r,m), and in the water (r) . The fact should be empha- sized that temperature is not 'measured' in the proper sense — the volume is measured; va have simply defined a method for giving a number to temperature. In ordinary laboratory practice niereury-iu-glass tliermometers are used; and divisions with numbers are marked on them, which are designed to correspond to proportionate increases in volume. These numbers have no meaning until the instrument is compared with a hj-drogen thermometer; and a table of values connecting the numbers and the true tempera- tures — as defined above — is prepared. See Ther- mometer. Mechanical Equivalent of Heat, Since, in practice, heat-effects are rarely produced by mechanical work, the erg is not a convenient unit in terms of which to measure heat-energy. Almost invariably the energy required to produce a given heat-cfl'ect or the energy given out when the opposite effect occurs, is measured in terms of the change in temperature of water : thus, to find how much energy is required to make ice melt, a quantity of ice of known mass is put into a known mass of water at a known temperature, and the fall in temperature is observed. There- fore a practical unit for the measurement of heat- energy is the "energy required to raise the tem- perature of one gram of puie water from 15° to 16° Centigrade;" this is called the 'calorie.' The limiting temperatures must be defined, be- cause it is not necessarily true that the same amount of energy would raise the temperature of one gram of water from 10° to 11°, or from 60° to 61°. as from 15° to 10° — in fact, it does not. This definition of a practical unit for measuring heat-energy is not an ideal one, because it makes the unit of energv' depend upon so many extra- neous conditions, viz. all those involved in the definition of temperature. It would be much better theoretically to choose some heat-effect which is independent of temperature, e.g. the energy required to make one gram of water boil away at normal atmospheric pressure ; but such a unit could not be used practically. Experi- ments show that the amoinit of energy required to raise the temperature of one gram of water one degree at any temperature is nearly one calorie; and so for all practical purposes this is assumed. The number of ergs equivalent to one calorie has been called the 'mechanical equivalent of heat.' Its value is 4.187 X 10', according to the best determinations. There are in general two experimental methods for measuring this most important quantity: a mechanical one, depend- ing upon the production of the rise of tempera- ture of the water by a paddle revolving in it; an electrical one, in which the rise in temperature is produced by the heating effect of an electric current. In the first method the amoimt of w-ork done is measured directly in ergs by a suitable dynamometer: in the second, the electrical quan- tities, current resistance, and electro - motive force are measured and the number of ergs cal- culated (energy = Et/). (See Electricity.) The mechanical method was first used accurately by .Toule (1843-45), and more recently by Row- hind (1878), and by Reynolds and Moorby (1897). (The last two investigators did not measure the calorie directly, however.) The electrical method was also first used by Joule; and within recent vears it has been perfected by Grifl^ths (1893), Schuster and G.annon (1894), and Callendar and Barnes (1899). (For a full discussion of these experiments reference should be made to an article by Ames in Reports of the
