28, 29] Mass Motion and Molecular Motion 29 



29. Equation (32) expresses that the total energy of a gas may be 

 regarded as the sum of the energies of a mass-motion and a molecular 

 motion. In the language of the older physics, one would say that the total 

 energy was partly kinetic and partly thermal. In the language of the 

 Kinetic Theory, both energies are equally kinetic. 



Let us suppose that the containing vessel, which has so far been moving 

 with a velocity of which the components are u 0> v , w , is suddenly brought 

 to a standstill. This will of course destroy the steady state of the gas, but 

 after a sufficient time, the gas will assume a new and different steady state. 

 The mass-velocity of this steady state will obviously be nil, and the energy 

 wholly molecular. The individual molecules have not been acted upon by 

 any external .forces except in their impacts with the containing vessel, and 

 these leave their energy unchanged. The new molecular energy is therefore 

 equal to the former total energy. These data enable us to determine the 

 new steady state. In the language of the older physics, one would say that 

 by suddenly stopping the forward motion of the gas the kinetic energy of 

 this motion had been transformed into heat. In the language of the Kinetic 

 Theory, we say that the total kinetic energy has been redistributed, so as 

 now to be wholly molecular. 



An interesting region of thought, although one outside the domain of 

 pure Kinetic Theory, is opened up by the consideration of the processes by 

 which this new steady state is arrived at. To examine the simplest case, 

 let us suppose the gas to be contained in a cubical box, and to have been 

 moving originally in a direction perpendicular to one of the sides. The 

 hydrodynamical theory of sound is capable of tracing the motion of. the gas 

 throughout all time, subject of course to the assumptions on which the theory 

 is based. The solution obtained to the problem from the hydrodynamical 

 standpoint is that the original motion of the gas is perpetuated in the form 

 of plane waves of sound in the gas, the wave fronts all being perpendicular to 

 the original direction of motion. This solution is obviously very different 

 from that arrived at by the Kinetic Theory. For instance, the solution 

 of hydrodynamics indicates that the original direction of motion remains 

 differentiated from other directions in space through all time, whereas the 

 solution of the Kinetic Theory indicates that a state is soon attained in which 

 there is no differentiation between directions in space. 



The explanation of the divergence of the two solutions is naturally to be 

 looked for in the differences of the assumptions made. The conception of 

 the perfect non-viscous fluid postulated by hydrodynamics is an abstract 

 ideal which is logically inconsistent with the molecular constitution of matter 

 postulated by the Kinetic Theory. Indeed we shall in a later part of the 

 book be able to shew that the actual viscosiuy of gases is simply and fully 

 accounted for by their molecular structure. If we introduce viscosity terms 



