22 WILSON AKT. c 



and q" — q' = w we must have Q" = mq", which proves the 

 theorem.* 



Lecture VI. The first and second laws may be used to define 

 a thermometric scale. For any two engines working between 

 the same temperatures tx and h the heats received and given up 

 satisfy the proportion 



Qi qx 



and hence these ratios may be taken as ti/ti. Thus 



ti Qi U Qs 1 .1 <• Q^ ^3 



- = — , ~ ~ TT' ^^^ therefore 7^" = ""• 

 ti Qi ti Qi Qi ti 



This shows that t may be taken as proportional to Q or 



Q._Qy 



This is called the absolute thermodynamic scale and the only 

 remaining freedom is to define the unit. 



The first law is not confined to reversible cycles but the second 

 law is. If we have two engines with 



Q" — Q' = W (reversible or not) and q" — q' = W (reversible) 

 and run the second backward so that no work is done, the net 

 heat Q" — q" leaves the higher temperature and the equal 

 amount Q' — q' is received at the lower temperature. As heat 

 cannot go without work from lower to higher temperature, Q" 

 - q" = Q' - q' ^0. Hence 



Q" - q" ^ Q' -q' 

 t" - t' ' 



the equahty sign holding only when the numerators vanish, i.e., 

 for the reversible case. But as q"/q' = t"/t' we have 



Q" Q' 



-7;- ^ -7 for any cycle. 



* The slow development of the analytical part of the subject was note- 

 worthy. It was Gibbs' intention that the student should thoroughly 

 grasp the physical, historical, and logical background through ample 

 discussion. 



