112 Dr. R. D. Kleeman on the Kinetic 



Then, since the temperature gradient is unity, ] , - =1. Tt 



2 



should be noticed that the molecule need not necessarily 

 retrace its path after having traversed the distance l 2 . Let 

 us suppose that the motion of the molecules takes place 

 parallel to three directions at right angles to one another, 

 one of which is parallel to the flow of: heat. Let n 2 molecules 

 cross per second a plane 1 cm. 2 in area situated at right 

 angles to the flow of heat and passing through the end of 

 the molecular path l 2 . Now when a number of molecules 

 move in the direction of the flow of heat, they not only part 

 with a portion of their original kinetic energy to the sur- 

 rounding molecules, but also with potential energy due to 

 molecular attraction, etc., since they become more densely 

 congregated. At the same time they gain heat due to the 

 external work done when undergoing compression ; this work 

 is done by the surrounding molecules; but an equivalent 

 amount of energy is handed over to them again on equali- 

 zation of temperature. Thus, in the latter case, there is, on 

 the whole, neither gain nor loss of heat. The amount of heat 

 gained per cm. 2 per second in the plane in question, when n 2 

 molecules cross it in the direction of the flow of heat, is 

 therefore n 2 (*i — h) wy or "l>^2 ? >*"7> where 7 is the internal 

 specific heat per gram of substance at constant pressure, and 

 m a the absolute molecular weight of a molecule. This gain 

 of heat is the conductivity 0, or 



C = ! s m a y(^±Py (5) 



on substituting for n 2 the same value as for ?? x in the previous 

 section. 



The mean free path l x and l 2 of a molecule relating to 

 viscosity and conduction of heat respectively have very 

 different meanings when the matter is so dense that P M is 

 comparable in magnitude with p. The quantity l A then 

 denotes the distance a molecule traverses till it has a certain 

 component of motion at right angles to its original motion, 

 the minimum kinetic energy remaining unchanged. The 

 quantity l 2 denotes the distance traversed till its minimum 

 kinetic energy has decreased to that of a molecule of the 

 surrounding matter, but during its journey it was receiving 

 energy from changes in the potential energy due to mole- 

 cular attraction, &c. The ratio of Z 2 to l 2 is given by the 

 equation 



l -'~% (6) 



h C 



