DIFFUSION AND ENTROPY OF GASES 60 1 



A into the vertical position. In that we spend work MgAC, if 

 M be the mass of the gas. We need not take into account the 

 mass of the tube. 



Process (2). Set the pistons free, then compression ensues 

 towards the base. The centre of gravity falls to C . We gain 

 work from gravity MgQC, which is all spent in the compression. 



Process (3). Again fix the pistons, and turn the tube about 

 A into the horizontal position. In that we gain work MgAQ. 



Process (4). Let the gas expand till it reaches its initial 

 uniform density. In that we gain work by the expansion equal 

 to the work spent in compression, that is MgdC. 



In all we have spent work MgAC in (1) and gained work 

 MgAC x in (3) and MgdC in (4) — that is, we have spent zero 

 work. 



8. Case II. — Instead of a single gas, let there be in the hori- 

 zontal tube equal numbers of molecules of oxygen and hydrogen 

 uniformly mixed, then insert and fix the pistons, and perform 

 Process (1) as before. In that we spend work MgAC as before, 

 M being the combined mass of the gases. 



Process (2). Set the pistons free, and compression takes 

 place as before. The c g falls to C, and the work of com- 

 pression, which is done by gravity, is MgCC. 



Before Process (3) we must now interpolate a new process 

 (2a) — namely, remove the pistons, so that diffusion takes place. 

 The gases assume a new position of equilibrium, in which each 

 behaves as a vacuum to the other. 



If Rj denote the density per unit of volume for oxygen at the 

 base, r x its density at height s, and if R 2 , r 2 be the corresponding 

 densities of hydrogen, r x = R 1 e- 2hm,gs , and r 2 = R 2 e- 2hm;;gs , m x 

 being the mass of a molecule of oxygen, m 2 that of hydrogen 

 — that is, oxygen partially replaces hydrogen in the lower, 

 hydrogen replaces oxygen in the upper strata. The centre of 

 gravity falls to C". Before considering what becomes of the 

 work thus gained MgC'C", let us perform Processes (3) and (4). 

 Fix the pistons, Process (3), and turn the tube about A into the 

 horizontal position. In that we gain work MgAC". 



Up to this point we have spent work MgAC, and gained 

 MgAC". 



Then Process (4), set free the pistons, and let the gases 

 expand without diffusion till they attain uniform pressure, but 

 not uniform mixture, throughout the tube. The work gained in 



