652 



SCIENCE. 



[N. S. Vol. II. No. 46. 



difference in temperature. Or, in algebraic 

 language, 



H : H' : : T : T' 

 H : H-H' : : T : T-T' 



T-oy 



T 



Work, = H-H' 



.H 



This equation shows what fraction of the 

 heat may be converted, into work, under 

 the most favorable conditions; namely, the 

 fall in temperature divided by the ab- 

 solute temperature at which the heat is sup- 

 plied. 



My present purpose is to present this 

 topic in its bare outlines, and with the 

 gTcatest simplicity possible. Those who 

 wish to follow the deductive reasoning in 

 detail must use the notation of Calculus, 

 in accordance with the following steps. 

 Combining the formula for the total work 

 (as implied in the first law) with that for 

 work derived from change of temperature 

 (the second law) we deduce a differential 

 equation for the work obtained or required 

 in isothermal changes. The change under 

 consideration maj' involve external work, 

 as when a vapor or gas is generated against 

 atmospheric pressure; or it may be internal 

 work of different kinds, as when the mole- 

 cules are endowed with increased kinetic 

 energy in volatilizing, or when a compound 

 is decomposed into its constituents, with 

 increased potential energj^. 



A somewhat difficult but important paper 

 by J. Willard Gibbs* treats of the equilib- 

 rium of heterogeneous substances, giving 

 deductions from the two laws of thermo- 

 dynamics, which in turn become major 

 pi'emises for a host of further deductions ; 

 so broad, indeed, are the propositions of 

 Gibbs, that the distinctions between chem- 

 istry and physics do not appear; there may 

 be two ' heterogeneous substances ' of like 

 chemical nature, as water and its vapor; 



*Trans. Comi. Acad., 3, 108, 343(1874-78). See, 

 also, Amer. Jour. Sci. [3] 16, 441 (1877); 18,277 



(1878). 



there may be three chemical bodies, as 

 limestone with the lime and the carbon 

 dioxid obtained by ignition; or there may 

 be several phj^sical mixtures, as solution of 

 water in ether, solution of ether in water, 

 and the mixed vapor resting upon both 

 liquids. Now, a little consideration will 

 show the importance of knowing when 

 equilibrium is established, for this is equiva- 

 lent to saying that no further action can 

 take place; the solution is saturated, no 

 longer acting upon the salt ; or the gas 

 which has been generated under pressure 

 is no longer evolved. When a change takes 

 place spontaneously, as when I drop a 

 stone, or mix sulphuric acid with water, 

 heat is developed from some other form of 

 energy. To reverse the process, work must 

 be done. The conversion of heat into work 

 is limited hj natural law ; when a given 

 change implies the doing of work, and that 

 work is forbidden by the terms of our major 

 premise, the change is impossible, equilib- 

 rium prevails. 



' Osmotic pressure ' in dikite solutions is 

 analogous to the pressure of gases; the Gay- 

 Lussac-Marriotte law, with slight modifica- 

 tion of terms, applies to molecules in the 

 liquid state. If work is required to dimin- 

 ish the volume of a gas by means of pres- 

 sure, work is likewise required to diminish 

 the volume of a body in dilute solution, 

 whether the solvent be removed bj^ evapor- 

 ation or by freezing. Boiling point and 

 freezing point of the solvent are changed 

 bj-- the presence of the dissolved body. 

 The agreement of observed facts with the- 

 oretical deductions has led to important 

 methods of determining molecular weights, 

 while the apparent discrepancies in the 

 case of electrolytes have proved an im- 

 portant argument for the doctrine that 

 these compounds are dissociated into their 

 ions. 



Our Chairman has pointed out the mu- 

 tual indebtedness of technology and pure 



