﻿578 
  MR 
  W. 
  J. 
  M. 
  RANKINE 
  ON 
  THE 
  

  

  Equilibrium 
  of 
  heat 
  and 
  pressure 
  between 
  portions 
  of 
  two 
  different 
  perfect 
  

   gases 
  in 
  contact 
  requires 
  that 
  the 
  pressures 
  independent 
  of 
  heat, 
  and 
  the 
  pres- 
  

   sures 
  caused 
  by 
  heat, 
  shall 
  separately 
  be 
  in 
  equilibrio. 
  Let 
  the 
  suffixes 
  a 
  and 
  b 
  

   be 
  used 
  to 
  distinguish 
  quantities 
  relative 
  to 
  two 
  different 
  substances 
  in 
  the 
  per- 
  

   fectly 
  gaseous 
  condition. 
  Then 
  the 
  first 
  condition 
  of 
  equilibrium 
  is 
  expressed 
  as 
  

   follows 
  : 
  — 
  

  

  (t) 
  (a) 
  = 
  (t) 
  w 
  W 
  

  

  that 
  is 
  to 
  say, 
  the 
  densities 
  of 
  two 
  perfect 
  gases 
  in 
  equilibrio 
  are 
  inversely 
  propor- 
  

   tional 
  to 
  the 
  coefficients 
  of 
  elasticity 
  of 
  their 
  atomic 
  atmospheres. 
  

   The 
  second 
  condition 
  is 
  expressed 
  as 
  follows 
  : 
  — 
  

  

  which, 
  being 
  taken 
  in 
  connection 
  with 
  the 
  first 
  condition, 
  gives 
  

  

  (xQ)( 
  a 
  > 
  = 
  (i«)« 
  ( 
  92 
  -> 
  

  

  Now 
  by 
  Equation 
  90, 
  we 
  have 
  

  

  N 
  PV 
  

  

  Hence 
  the 
  condition 
  of 
  equilibrium 
  of 
  heat 
  between 
  two 
  perfect 
  gases 
  is 
  

  

  Gr) 
  w 
  - 
  (x) 
  « 
  w 
  

  

  consequently, 
  temperature 
  may 
  be 
  measured 
  by 
  the 
  product 
  of 
  the 
  pressure 
  and 
  vo- 
  

   lume 
  of 
  a 
  perfect 
  gas, 
  divided 
  by 
  a 
  coefficient, 
  which 
  is 
  proportional 
  to 
  the 
  volume 
  of 
  

   the 
  gas 
  at 
  a 
  standard 
  pressure 
  and 
  temperature. 
  

  

  Temperatures 
  thus 
  measured 
  are 
  reckoned 
  from 
  the 
  point 
  known 
  as 
  the 
  zero 
  

   of 
  gaseous 
  tension, 
  or 
  absolute 
  zero 
  of 
  a 
  perfect 
  gas 
  thermometer, 
  274°- 
  6 
  centigrade 
  

   below 
  the 
  temperature 
  of 
  melting 
  ice. 
  

  

  Let 
  V 
  denote 
  the 
  volume 
  of 
  unity 
  of 
  weight 
  of 
  a 
  perfect 
  gas, 
  at 
  a 
  standard 
  

   pressure 
  P 
  , 
  and 
  absolute 
  temperature 
  r 
  ; 
  then 
  any 
  other 
  absolute 
  temperature 
  

   has 
  the 
  following 
  value 
  : 
  — 
  

  

  W=P^ 
  (NQ 
  + 
  fc) 
  (94.) 
  

  

  T 
  = 
  

  

  while 
  the 
  absolute 
  temperature 
  of 
  total 
  privation 
  of 
  heat 
  is 
  

  

  K 
  = 
  T 
  opv- 
  ( 
  94A 
  -) 
  

  

  r 
  o 
  v 
  o 
  

  

  Hence 
  it 
  appears 
  that 
  quantity 
  of 
  heat 
  in 
  unity 
  of 
  weight 
  bears 
  the 
  following 
  

   relation 
  to 
  temperature, 
  — 
  

  

  1 
  ,™ 
  « 
  P 
  n 
  V 
  n 
  

  

  Q=^(PV-A) 
  = 
  ^.«(t-k) 
  (95.) 
  

  

  o 
  

  

  