﻿396 
  Linebarger 
  — 
  Some 
  Relations 
  between 
  Temperature, 
  etc. 
  

  

  case 
  the 
  latent 
  heat 
  of 
  vaporization 
  of 
  the 
  liquid 
  under 
  exam- 
  

   ination 
  is 
  known, 
  this 
  correction 
  is 
  easily 
  made 
  by 
  the 
  applica- 
  

   tion 
  of 
  equation 
  (1), 
  which 
  gives 
  in 
  terms 
  of 
  latent 
  heat, 
  tem- 
  

   perature, 
  and 
  volume, 
  the 
  change 
  of 
  the 
  boiling 
  point 
  with 
  the 
  

   concomitant 
  variation 
  of 
  pressure. 
  But 
  the 
  latent 
  heats 
  of 
  

   volatilization 
  are 
  known 
  for 
  only 
  a 
  comparatively 
  small 
  number 
  

   of 
  liquids. 
  In 
  this 
  case, 
  the 
  "law" 
  treated 
  of 
  in 
  the 
  fore- 
  

   going 
  sections 
  is 
  specially 
  applicable. 
  We 
  know 
  from 
  what 
  

   precedes 
  that 
  near 
  atmospheric 
  pressure 
  

  

  ^- 
  = 
  const., 
  (A) 
  

  

  The 
  " 
  constant 
  " 
  varying 
  slightly 
  for 
  different 
  classes 
  of 
  

   liquids 
  from 
  an 
  average 
  value 
  of 
  20*7, 
  at 
  least, 
  for 
  normal 
  

   liquids. 
  If 
  we 
  set 
  for 
  the 
  " 
  constant," 
  the 
  letter 
  C, 
  neglect 
  

   the 
  volume 
  of 
  the 
  liquid 
  in 
  comparison 
  with 
  that 
  of 
  the 
  vapor 
  

   — 
  which 
  will 
  introduce 
  no 
  appreciable 
  error, 
  — 
  and 
  substitute 
  for 
  

  

  T 
  its 
  equal 
  ^L 
  , 
  equation 
  (1) 
  becomes 
  transformed 
  into 
  

  

  dp-~C' 
  (B) 
  

  

  If 
  now, 
  from 
  the 
  gas 
  equation 
  

  

  2T 
  

  

  v=z 
  — 
  (C) 
  

  

  p 
  v 
  } 
  

  

  we 
  take 
  the 
  value 
  of 
  jutp 
  (pp 
  = 
  Y 
  = 
  a 
  gram-molecule 
  of 
  satu- 
  

   rated 
  vapor), 
  and 
  set 
  it 
  in 
  equation 
  (B), 
  we 
  obtain 
  the 
  equality 
  

  

  ^ 
  = 
  ^- 
  (D) 
  

  

  dp 
  pC 
  

  

  and 
  if 
  p 
  be 
  the 
  normal 
  pressure 
  of 
  760 
  mm 
  , 
  we 
  get 
  finally 
  

  

  ^■"760C~"380C' 
  W 
  

  

  or 
  

  

  By 
  putting 
  for 
  C, 
  that 
  value 
  of 
  the 
  constant 
  found 
  for 
  the 
  

   class 
  of 
  liquids 
  to 
  which 
  the 
  liquid 
  under 
  examination 
  belongs 
  

   (see 
  page 
  359), 
  and 
  for 
  T, 
  the 
  absolute 
  temperature 
  of 
  ebullition, 
  

   we 
  may 
  obtain 
  with 
  a 
  very 
  considerable 
  degree 
  of 
  accuracy 
  the 
  

   desired 
  correction, 
  with 
  the 
  restriction, 
  however, 
  that 
  the 
  

   variation 
  of 
  pressure 
  is 
  but 
  slight, 
  that 
  is, 
  not 
  over 
  50 
  milli- 
  

   meters 
  of 
  mercury. 
  

  

  Chicago, 
  January 
  22d, 
  1895. 
  

  

  