227-229] 



Mechanical Illustrations 



191 



a dissipation function (represented by conduction of heat through the wall 66'), 

 while the former was not affected by a direct dissipation function but lost 



FIG. 13. 



energy by transfer represented by conduction through the channel C. We may, 

 therefore, suppose the actual physical temperatures of A and B to correspond 

 to the principal and subsidiary temperatures, say T and r, of a gas which has 

 only one subsidiary temperature. 



From a general knowledge of physics we can see what will ultimately 

 happen to this system. According as T is greater or less than T at any 

 instant, there will be conduction from A to B or from B to A through the 

 channel C. If the conduction through the channel C is good, the tempera- 

 tures will rapidly equalise, and the system tends to approach a state defined 

 by the equation T r. There is, however, a constant loss of energy through 

 the conducting wall bb' so that T continually decreases. The value of T also 

 decreases, lagging behind T by an amount which depends on the goodness of 

 conduction through the channel C. The coefficient of conduction through 

 the channel C will however decrease as T and r decrease, for the coefficient 

 of conduction in a uniform gas is proportional to some positive power of its 

 absolute temperature. Hence, however good or bad the conducting power 

 of the wall bb' may be, there will come a time, after the gas has cooled 

 sufficiently, when the wall bb' will be a good conductor in comparison with 

 the channel G. The conditions are now changed. A small quantity of heat 

 escapes from A through the channel C but is immediately lost through the 

 wall bb', and it is impossible for the value of T to attain to any appreciable 

 value. Here then we have the final (normal) state of the system. It is 

 a state in which T is finite but small and both T and dT/dt are, in the limit, 

 vanishingly small. 



This state is, moreover, analogous to that which observation shews to be 

 the state of a real gas under normal conditions, namely a state in which all 

 the energy is absorbed by a few degrees of freedom, corresponding to the 

 principal temperature, and in which the rate of dissipation is extremely 

 small. The illustration can be extended to apply to a gas with a large 

 number of subsidiary temperatures by imagining a large number of chambers 

 similar to B opening out of A, each by a separate channel. 



