34 MOLECULAR MOTION AND ITS ENERGY 18 



attain a greater speed on rebound from the moving piston 

 0an if they strike it when fixed. But since the kinetic 

 Venergy of the molecular motion is nothing but heat, it is 

 obvious that the compressing motion of the piston com- 

 municates heat to the gas. 



The reverse occurs when the pressure on the piston is so 

 small as to be overcome by the impacts of the molecules. 

 The piston then moves in the same direction as the mole- 

 cules that strike it, which therefore attain a less speed by 

 the impact, as they give part of their former momentum to 

 the piston. The gas consequently cools in doing work by 

 pushing the piston out. 



In this way the heating of a gas by compression was 

 explained by Kronig 1 and Clausius. 2 A mathematical 

 theory of the phenomenon has been given byWoldemar 

 Voigt. 3 



It has been shown by Clausius that the heat pro- 

 duced by pressure can easily be calculated on the grounds 

 of our theory, and that it is equal to the work done. In 

 a rather later memoir 4 he gives a proof which we here re- 

 produce. 



We will, for simplicity, continue to use Joule's pro- 

 cedure, described in 10, and therefore assume not only that 

 all molecules possess the same mean speed G, but also that 

 only one-third of the molecules are to be taken into account 

 in calculating the impacts on a wall of the containing 

 vessel. This assumption is admissible if the compression 

 takes place so slowly that the disturbance of the equilibrium 

 has always time at once to subside. With this supposition 

 the number of molecules which in unit time meet unit area 

 of the wall of the vessel is %NG, by 12, and the number 

 therefore in unit time which strike the surface F of the 

 piston is 



1 Grundzuge einer Theorie der Gase, 1856 ; also Pogg. Ann. xcix. 1856, p. 315. 



2 Pogg. Ann. c. 1857, p. 365 ; Abhandl. pi. 2, 1867, p. 242. 



3 Gott. Nachr. 1885, No. 6, p. 228. See Natanson, Wied. Ann. 1889, 

 xxxvii. p. 341. 



4 Mech. Warmetheorie, iii. 1889-91, 14, p. 29. 



