SECOND LAW OF THERMODYNAMICS 237 



resented by the transfer of heat from a given high temperature T 1 to 

 a given low temperature T 2 is proportional to the quantity of heat 

 transferred. Consider a steady flow of heat from temperature T 1 to 

 temperature T 2 constituting a steady sweep, a sweep which remains 

 entirely unchanged in character in successive intervals of time. Any 

 result of this sweep must be proportional to the lapse of time, and 

 therefore the degeneration which takes place in a given interval of 

 time is proportional to the time; but the quantity of heat transferred 

 is also proportional to the time, therefore, the amount of degeneration 

 is proportional to the quantity of heat transferred from temperature 

 T x to temperature T 2 . 



Kelvin's Definition of Temperature Eatio 



The definition of the ratio of two temperatures previously given 

 was understood to be a provisional definition. We are now in a posi- 

 tion to propose a definition of the ratio of two temperatures which is 

 independent of the physical properties of any particular substance. 

 This definition will remain somewhat vague, however, until the action 

 of the steam engine is discussed in the later sections of this article. 

 According to proposition (a) above, the thermodynamic degeneration 

 which is involved in the conversion of work into heat at a given tem- 

 perature is proportional to the amount of work so converted and the 

 proportionality factor depends upon the temperature only. There- 

 fore, we may write 



«£' = m JV (2) 



and 



^" = m 2 W (3) 



where <f>' is the degeneration involved in the conversion of an amount 

 of work W into heat at temperature T 1} and <£" is the degeneration 

 involved in the conversion of an amount of work W into heat at tem- 

 perature To, and m 1 and m 2 are factors which depend only upon T x 

 and To, respectively. The amount of work W having been converted 

 into heat at temperature T 1; imagine the heat to flow to a lower tem- 

 perature T 2 , thus involving an additional amount of degeneration 

 according to proposition (b) above. The conversion of work W into 

 heat at temperature T x and the subsequent flow of this heat to a lower 

 temperature T 2 gives the same result as would be produced by the 

 conversion of the work into heat at the lower temperature directly. 

 Therefore the lower the temperature at which work is converted into 

 heat the greater the amount of degeneration involved. That is to say, 

 the factor ra 2 in equation (3) is larger in value than the factor m 1 



