﻿Jheory 
  of 
  the 
  Thermoelectric 
  Forces. 
  773 
  

  

  Suppose 
  N„/Nj 
  to 
  be 
  independent 
  of 
  the 
  temperature, 
  then 
  

  

  4, 
  N„ 
  

  

  JU-jkgjfc[.fr-*], 
  

  

  the 
  thermoelectromotive 
  force 
  would 
  be 
  proportional 
  to 
  the 
  

   difference 
  of 
  temperature, 
  and 
  would 
  only 
  depend 
  on 
  the 
  

   potential-differences 
  o£ 
  contact 
  at 
  the 
  temperatures 
  T' 
  and 
  T. 
  

   If 
  one 
  single 
  corpuscle 
  passes 
  round 
  about 
  the 
  thermoelectric 
  

   circuit, 
  the 
  force 
  E 
  will 
  perforin 
  an 
  amount 
  of 
  electric 
  work 
  

   equal 
  to 
  E 
  . 
  e. 
  Neglecting 
  a 
  certain 
  factor 
  this 
  work 
  is 
  equal 
  

   to 
  the 
  difference 
  of 
  the 
  values 
  which 
  the 
  quantity 
  aT 
  

   possesses 
  at 
  the 
  temperatures 
  T 
  and 
  T'. 
  The 
  difference 
  

   aT' 
  — 
  aT 
  is 
  the 
  increase 
  in 
  the 
  mean 
  kinetic 
  energy 
  of 
  a 
  

   molecule 
  of 
  gas, 
  which 
  is 
  heated 
  from 
  the 
  temperature 
  T 
  to 
  

   the 
  temperature 
  T'. 
  

  

  If 
  we 
  study 
  the 
  electromotive 
  force 
  produced 
  by 
  a 
  standard 
  

   metal, 
  for 
  instance 
  lead 
  combined 
  with 
  any 
  other 
  metal 
  a, 
  

   we 
  may 
  represent 
  the 
  electromotive 
  force 
  as 
  a 
  function 
  of 
  

   the 
  temperature 
  difference 
  in 
  the 
  following 
  way 
  : 
  

  

  u 
  a 
  and 
  fia 
  are 
  the 
  temperature 
  coefficients 
  of 
  the 
  metal 
  a 
  ; 
  

   combining 
  the 
  standard 
  metal 
  with 
  any 
  other 
  metal 
  b 
  we 
  

   find: 
  

  

  a 
  h 
  and 
  ft 
  b 
  are 
  the 
  first 
  and 
  second 
  coefficients 
  of 
  temperature 
  

   of 
  the 
  metal 
  b. 
  If 
  two 
  metals 
  a 
  and 
  b 
  form 
  a 
  thermo- 
  

   element, 
  one 
  junction 
  of 
  which 
  is 
  at 
  the 
  temperature 
  t, 
  the 
  

   other 
  at 
  0° 
  C, 
  the 
  thermoelectric 
  force 
  will 
  be 
  found 
  to 
  be: 
  

  

  E 
  

  

  = 
  K-^)*+(^^V, 
  

  

  or 
  

  

  E= 
  (a 
  a 
  _^)(T-273)+(^^)(T-273) 
  2 
  , 
  

   T 
  being 
  the 
  absolute 
  temperature. 
  

  

  5? 
  = 
  1 
  1 
  log 
  J 
  = 
  a 
  "~ 
  ab 
  + 
  (/3 
  « 
  -/36) 
  (T 
  _ 
  273) 
  

  

  N„ 
  !;[a<.-a/,+(j3«-/3i,)(T-273)]. 
  

  

  