60 PROCEEDINGS OP THE AMEEICAN ACADEMY. 



4. Every solution diluted indefinitely approaches a limiting condition 

 in which 



Tlv = RT, (2) 



if n represents osmotic pressure. 



The present paper will discuss the laws which govern systems com- 

 posed of a single, chemically simple, substance, and will be followed by a 

 second paper in which the laws governing mixtures will be studied. 



I. 



Clausius' Formula Simplified. 



Clausius showed that if Q represents the heat change in a reversible 

 change, the second law of thermodynamics may be expressed by the 

 equation 



Q _dQ 



'T~'dT' (^) 



which is valid for every cyclic process ; moreover, that since in a cycle 

 there is no change in internal energy, d Q represents the work of the 

 cycle, and that when the process is one in which the system undergoes a 

 finite change of volume at constant pressure, and no other work is done, 



where P represents the pressure and Vx and Vo, the original and final 

 volumes. In the specific case in which the system is composed of a 

 liquid and its vapor we obtain the equation 



Q _ (vi — ^2) dp 

 T~ dT ' 



in which p represents vapor pressure ; Q, the total heat of vaporization 

 of one gram-molecule ; and Vj and Vo, the molecular volumes of vapor and 

 liquid respectively. Transposing the equation gives an expression for 

 the change of vapor pressure with change of temperature, 



dp _ Q 



dT- (v,- V,) T ' (^) 



This equation of Clausius is both general and exact, but in practice it 

 is replaced by a simpler equation, which is derived from it if two 

 assumptions are made : First, that v^ is negligible compared with Vi, and 

 therefore approximately, 



ri — ^2 = Vx- 



