and the Laws regarding the Nature of Heat. 5 



brought at the conclusion into its original state, the sum of its 

 sensible and latent heats must, according to the above assump- 

 tion, be the same as before ; hence, if during any portion of the 

 process heat be communicated from without, the quantity thus 

 received must be given off again during some other portion of 

 the process. With every alteration of volume, however, a certain 

 quantity of work is either produced or expended by the gas ; for 

 by its expansion an outward pressure is forced back, and on the 

 other hand, compression can only be effected by the advance of 

 an outward pressure. If, therefore, alteration of volume be 

 among the changes which the gas has undergone, work must 

 be produced and expended. It is not, however, necessary that at 

 the conclusion, when the original condition of the gas is again 

 established, the entire amount of work produced should be exactly 

 equal to the amount expended, the one thus balancing the other ; 

 an excess of one or the other will be present if the compres- 

 sion has taken place at a lower or a higher temperature than the 

 expansion, as shall be proved more strictly further on. This 

 excess of produced or expended work must, according to the 

 maxim, correspond to a proportionate excess of expended or pro- 

 duced heat, and hence the amount of heat refunded by the gas 

 cannot be the same as that which it has received. 



There is still another way of exhibiting this divergence of our 

 maxim from the common assumption as to the total heat of bodies. 

 When a gas at /q and Vq is to be brought to the higher tempera- 

 ture ^j and the greater volume Vj, the quantity of heat necessary to 

 effect this would, according to the usual hypothesis, be quite in- 

 dependent of the manner in which it is communicated. By the 

 above maxim, however, this quantity would be different according 

 as the gas is first heated at the constant volume v^ and then per- 

 mitted to expand at the constant temperature t-^, or first expanded 

 at the temperature ^q and afterwards heated to t^ ; the quantity 

 of heat varying in all cases with the manner in which the altera- 

 tions succeed each other. 



In like manner, when a quantity of water at the temperature 

 tQ is to be converted into vapour of the temperature t^ and the 

 volume ^1, it will make a difference in the amount of heat neces- 

 sary if the water be heated first to t^ and then suffered to evapo- 

 rate, or if it be suffered to evaporate by t^ and the vapour heated 

 afterwards to t^ ; or finally, if the evaporation take place at any 

 intermediate temperature. 



From this and from the immediate consideration of the maxim, 

 we can form a notion as to the light in which latent heat must 

 be regarded. Referring again to the last example, we distin- 

 guish in the quantity of heat imparted to the water during the 

 change the sensible heat and the latent heat. Only the former 

 of these, however, must we regard as present in the produced 



