; ; DIFFUSION. 



and pfOMuro is equal to that which would be produced in the mixture by 

 taking away a quantity of heat equivalent to this work. 



i: the diffusion takes place by an irreversible process, such as goes on 

 when the gates are placed together in a vessel, no external work is done, 

 and there is BO fall of temperature or of pressure during the process. 



We may arrive at this result by a method whkh, if not so instructive 

 a* that of Lord Rayleigh, is more general, by the use of a physical quantity 

 called by Clausius the Entropy of the system. 



Hie entropy of a body in equilibrium is a quantity such that it remains 

 constant if no heat enters or leaves the body, and such that in general the 

 quantity of heat which enters the body is 



where <f> is the entropy, and 6 the absolute temperature. 



The entropy of a material system is the sum of the entropy of its parts. 



In reversible processes the entropy of the system remains unchanged, but 

 in all irreversible processes the entropy of the system increases. 



The increase of entropy involves a diminution of the available energy of 

 the system, that is to say, the total quantity of work which can be obtained 

 from the system. This is expressed by Sir W. Thomson by saying that a 

 certain amount of energy is dissipated. 



The quantity of energy which is dissipated in a given process is equal to 



W.-6), 



where & is the entropy at the beginning, and <, that at the end of the 

 process, 'and 0. is the temperature of the system in its ultimate state, when 

 1 1' i more work can be got out of it. 



When we can determine the ultimate temperature we can calculate the 

 amount of energy dissipated by any process; but it is sometimes difficult to 

 do this, whereas the increase of entropy is determined by the known states 

 of the system at the beginning and end of the process. 



The entfopy of a volume v l of a gas at pressure p l and temperature l 

 exceeds its entropy where its volume is v t and its temperature 0, by the quantity 



Hence if volumes r, and i\ of two gases at the same temperature and pressure 



