Intelligence and Miscellaneous Articles. 237 



and at the same temperature T ; secondly, the same gases are mixed, 

 at the same temperature, in the space Vi + V 2 , while the total pres- 

 sure is equal to the previous pressure of each separate gas. In the 

 first case let E, be the entropy of the first, E 2 that of the second 

 gas ; in the second case let E, 2 be that of the mixture. According 

 to the rule given above, E x , E 2 , and E 12 can be calculated by means 

 of the above formula. We thus find 



T(E 12 -E 1 -E 2 )=T(y'-y)[(v 1 +y 2 y(Y } +y 2 )-y 1 ^ i: -y 2 zv 2 ]. 



But this is the expression for the quantity of heat which can be 

 converted into work without any other compensation than the mix 

 ture of the two gases. Therein is y' — y the product of the weight 

 of unit volume into the difference of the two specific heats, which 

 product has the same value for both gases. 



The total work which can be gained from this heat is, according 

 to known principles, 



To gain this total work, of course we should not have recourse to 

 the expedient of diffusion through porous partitions, but convey the 

 one gas into the other by means of a substance that chemically com- 

 bines with one of the gases under partial dissociation (as quick-lime 

 with carbonic acid), of course taking care that the process always 

 remains reversible. We should, for example, first indefinitely 

 expand the first gas, then with the substance above mentioned 

 transfer it very slowly into the other, while, again, it would be 

 continually compressed so that the partial pressure of the first gas 

 was always equal in both vessels. Lastly, the mixture of gases 

 must be so far expanded that its volume shall be equal to the sum 

 of the volumes of the original gases. Since all these processes can 

 easily be accompanied by calculation, it will be easy in this way to 

 verify the above-given formula. — Kaiserliclie Akademie der Wissen- 

 schaften in Wien, matJiematisch-natiirwissenscJiaftliche Classe, June 6, 

 1878. 



ON THE RELATION OF THE WORK PERFORMED BY DIFFUSION TO 

 THE SECOND PROPOSITION OF THE MECHANICAL THEORY OF 

 HEAT. BY PROF. R. CLAUSIUS. 



In ' Nature ' for January 1878 (vol. xvii. p. 202), Mr. Tolver 

 Preston has specified a process by means of which mechanical work 

 can be gained through diffusion of gases. The reflections he makes 

 upon this fact are very ingenious, and in relation to theory very 

 interesting on account of the conclusions to which they give occa- 

 sion ; only m one point I think I must express a view different 

 from his : he thinks, namely, that the result of his process contra- 

 dicts the second proposition of the mechanical theory of heat ; and 

 in this I cannot coincide. 



The substance of his process is as follows. He imagines a cy- 

 linder divided into two sections by a movable piston. The piston 

 consists of a porous substance, such as pipe-clay or graphite. In 

 the two divisions of the cylinder two different gases are present, 

 oxygen and hydrogen for instance. 



