THERMODYNAMICS AND HEAT ENGINES Definitions of Symbols.—The principal physical properties of the working fluid with which we are concerned in the case of heat-engines are the specific volume V, the intrinsic energy E, the total heat H and the entropy 4), all of which are measured per unit mass of the substance considered. The laws of thermo dynamics require certain general relations between these prop erties and their derivatives, as affected by additions of heat Q per unit mass, or by variations in the imposed conditions of tempera ture T and pressure P. It should be observed that in all these relations P is the absolute pressure and not the gauge-pressure; and that T is measured on the absolute scale, as defined by Carnot's principle which differs very little from absolute tempera ture on the scale of a gas thermometer. Temperature measured on the same scale from o° C is denoted by t, so that T=t+273.1°. The total heat H is defined as E+aPV in thermal units, including the equivalent aPV of the work PV done by the pressure P on the volume V of unit mass. The entropy 4) of a quantity of heat Q supplied at a temperature T is defined as Q/T. The entropy of a substance per unit mass is the property which remains con stant in adiabatic expansion, when no heat is supplied by friction or otherwise, as will be more fully explained in a later section, in connection with the second law of thermodynamics.
heat-engines is to measure Q, E, and H in thermal units per unit mass, and to reduce W to thermal units by dividing by the appropriate value of the mechanical equivalent J. In nearly all cases W represents work done by expansion against a uniform pressure P, in which case IV =P( V— if P remains constant during the expansion, and equation (I) takes the form where the total heat H is defined as E-}-aPV, and a is the factor required for reducing PV to heat units per unit mass. The factor required for this purpose in practice is seldom I/J, because pressure-gauges are never graduated in lb./sq.ft. or kg./sq.m., but often in arbitrary units such as inches of mercury.
Specific Heats.—If the heat Q is added at constant volume, and W=o, so that Q=E—E.. If T—T. is the rise of temperature, we observe that the increase of E per degree at constant volume V. is equal to QAT—T.), which is by definition the specific heat S at constant volume. Similarly (H —H.)/ (T —T„) from (2) is equal to the specific heat S at constant pressure. Thus the values of E along a line of constant volume on any diagram may be found from observations of the specific heat s at constant volume. Similarly values of H along a line of constant pressure may be deduced from observations of the specific heat S at constant P.
These simple relations between H and S, and E and s, are exact for all substances at all temperatures in consequence of the definition of H, and are often very useful. But the specific heats S and s may vary widely with temperature and pressure, in which case it is usually better to measure H or E directly, in place of trying to deduce them from empirical formulae for S or s. In the case of solids or liquids, since V is small and varies little with T, the variation of E at constant pressure, such as atmos pheric, does not differ appreciably from that of H. But the variation of H at constant volume may greatly exceed that of E under the same condition on account of the high pressures developed. In practice it is usually preferable to measure the value of H and deduce that of E, if required, by subtracting aPV.