﻿Processes 
  and 
  Planck 
  9 
  s 
  Theory, 
  233 
  

  

  Tlie 
  Electromagnetic 
  Entropy. 
  

  

  14. 
  According 
  to 
  Planck's 
  definition, 
  the 
  entropy, 
  S, 
  of 
  the 
  

   resonator 
  whose 
  energy 
  is 
  U, 
  is 
  

  

  av\ 
  ^bv 
  J 
  

  

  av\ 
  

  

  where 
  a 
  and 
  b 
  are 
  constants. 
  It 
  is 
  independent 
  of 
  tho^ 
  

   entropy 
  of 
  the 
  incident 
  waves. 
  

  

  Again, 
  if 
  s 
  denote 
  the 
  entropy 
  per 
  unit 
  of 
  volume 
  of 
  a 
  

   monochromatic 
  wave 
  dfl 
  of 
  intensity 
  K 
  ? 
  we 
  have 
  by 
  analogy 
  

  

  to 
  art. 
  9, 
  s 
  = 
  dfl 
  - 
  , 
  where 
  

   ? 
  c 
  

  

  L= 
  ~^( 
  1 
  °^" 
  1 
  )' 
  

  

  which 
  has 
  a 
  determinate 
  value 
  at 
  every 
  point. 
  The 
  actual 
  

   entropy 
  of 
  any 
  given 
  volume 
  of 
  the 
  wave 
  throughout 
  which 
  

   Kis 
  constant 
  is, 
  oris 
  proportional 
  to, 
  the 
  last 
  expression 
  multi- 
  

   plied 
  by 
  the 
  given 
  volume. 
  

  

  15. 
  Up 
  to 
  this 
  point 
  I 
  have 
  closely 
  followed 
  Planck. 
  I 
  

   now 
  deviate 
  somewhat 
  from 
  his 
  method. 
  Let 
  /KdCldt 
  denote 
  

   as 
  before 
  the 
  energy 
  of 
  the 
  wave 
  of 
  intensity 
  K 
  which 
  passes 
  

   the 
  elementary 
  area 
  r 
  2 
  d£l 
  in 
  time 
  dt. 
  Then/ 
  is 
  proportional 
  

   to 
  the 
  volume 
  of 
  the 
  wave 
  in 
  question. 
  And 
  let 
  us 
  define 
  

   the 
  entropy 
  of 
  that 
  same 
  wave 
  as 
  follows 
  : 
  

  

  whence 
  ds 
  1 
  C 
  2 
  K 
  ^(/K) 
  ,_ 
  

  

  — 
  = 
  log 
  ; 
  —r 
  — 
  ; 
  — 
  -all. 
  

  

  dt 
  av 
  rt 
  bv 
  6 
  dt 
  

  

  Then 
  we 
  have 
  for 
  an 
  unpolarized 
  wave 
  

  

  d'. 
  1, 
  TJdTJ 
  1, 
  c*K 
  d(fK) 
  

  

  dt^ 
  + 
  ^ 
  = 
  -av 
  l 
  °ZbvW-a-v 
  ]0 
  Z-b?-dr' 
  

  

  But 
  

  

  dJJ 
  3c 
  2 
  <r/_ 
  v 
  2 
  U\ 
  . 
  ,. 
  

  

  ~-j- 
  = 
  - 
  — 
  ( 
  K 
  r 
  sin- 
  0, 
  

  

  dt 
  4l7tv 
  \ 
  c 
  J 
  

  

  and 
  

  

  

  dt 
  

  

  _ 
  3c 
  2 
  cr/v 
  2 
  U 
  

  

  47TV 
  V 
  c" 
  

  

  Therefore 
  

  

  

  

  d(S; 
  

  

  + 
  ')- 
  

  

  1 
  3 
  C 
  2 
  <7 
  . 
  s 
  

  

  sin 
  

  

  dt 
  av^—\T~V 
  l 
  ° 
  g 
  ^, 
  

  

  