310 . REPORTS ON THE STATE OF SCIENCE. 



Thermodynamic theory shows that the physical properties of a gas in 

 chemical equilibrium are completely specified when — 



(1) The relation between the pressure and volume at constant tem- 

 perature is known, and 



(2) The internal energy per unit volume is given as a function of the 

 temperature and the density. 



The energy of a gas per unit of mass at temperature 6 is usually 

 defined as k (6—Oq), where 6q is the standard temperature from which 

 energies are reckoned, and k the mean specific heat at constant volume 

 between the temperatures Oq and 6. The second of these data is there- 

 fore equivalent to a knowledge of the specific heat in terms of the 

 temperature and density. This form of statement is probably more 

 familiar ; but, for reasons given later on, it is in many ways less con- 

 venient than that based upon the energy function. 



For those gases with which we have to deal it may be assumed that 

 the first relation is that given by Boyle's Law. Experiment and theory 

 alike point to the conclusion that deviation from this law only occurs 

 when the density of the gas departs widely from its normal value, and 

 that it is diminished by high temperature. In the gas-engine the 

 density of the gas rarely exceeds ten times that of the atmosphere, a 

 point at which the deviation from Boyle's Law in air (at 100° C.) is 

 only about one-half per cent.^ 



It is usual to make the further assumption that the product pv is 

 proportional to the absolute temperature 6. A detailed examination of 

 the grounds of this assumption forms the subject of a section of this 

 report. At this point it is only necessary to notice that, if it be true, 

 then the internal energy is a function of the temperature only, and is 

 independent of the density. If, on the other hand, the perfect gas-law 

 does not hold, then the true relation between pv and 6 can be deduced 

 from a knowledge of the internal energy, which is in that case a function 

 both of the temperature and of the density. 



The properties of the gases with whicli we have to deal are therefore 

 completely defined when the energy has been tabulated as a function of 

 the temperature and the density. So far as the present state of know- 

 ledge goes the energy is to be expressed in terms of temperature only ; 

 but an important part of future investigation must deal with its 

 dependence on tlie density either by direct measurement or by a deter- 

 mination of the relation between pv and 6 at high temperatures. 



The prediction of the temperature reached in combustion, which 

 must be the starting-point of any investigation of explosions, also rests 

 primarily upon a knowledge of the energy function. For, subject to 

 corrections for loss of heat, incomplete combustion, and work done while 

 combustion proceeds, the thermal energy of the mixture of steam, COj, 

 &c., after combustion is equal to the chemical energy of the gases from 

 which that mixture was formed. The latter can be accurately inferred 

 from the composition of the combustible gases, and, the thermal energy 

 being thus known, the temperature can be calculated from a table of the 

 energy function. The pressure or volume changes resulting from com- 

 bustion can be deduced from the temperature by the use of the p—v—6 

 relations, which again ultimately depend upon the form of the energy 

 function. A table of this function at high temperatures is therefore 



' See Witkowski, Phil. Mag., vol. xli. (1896), p. 309. 



