﻿410 
  JOURNAL 
  OF 
  THE 
  WASHINGTON 
  ACADEMY 
  OF 
  SCIENCES 
  VOL. 
  12, 
  NO. 
  18 
  

  

  C-Pl 
  and 
  a 
  form 
  

  

  is 
  written 
  for 
  ( 
  ;— 
  ) 
  and 
  a 
  for 
  ( 
  — 
  — 
  ) 
  . 
  Values 
  of 
  both 
  m 
  and 
  a 
  

  

  for 
  the 
  more 
  common 
  gases 
  are 
  to 
  be 
  found 
  in 
  the 
  literature. 
  

  

  The 
  kerosene 
  referred 
  to 
  is 
  the 
  ordinary 
  commercial 
  product 
  having 
  

   a 
  density 
  of 
  about 
  0.8. 
  

  

  Probably 
  the 
  temperature 
  always 
  falls 
  in 
  isenergic 
  expansion 
  — 
  

   at 
  least 
  over 
  the 
  range 
  of 
  temperatures 
  and 
  pressures 
  which 
  have 
  

   hitherto 
  been 
  investigated. 
  This 
  is 
  equivalent 
  to 
  the 
  statement 
  that 
  

   the 
  internal 
  energy 
  of 
  a 
  substance 
  steadily 
  decreases 
  as 
  the 
  pressure 
  

   is 
  increased.^ 
  Isentropic 
  expansion 
  causes 
  a 
  fall 
  in 
  temperature, 
  

   except 
  in 
  those 
  rare 
  cases 
  wkere 
  the 
  expansion 
  coefficient 
  is 
  negative, 
  

   e. 
  g., 
  water 
  below 
  4° 
  C. 
  For 
  isenkaumic 
  expansion, 
  however, 
  there 
  

   is 
  no 
  such 
  regularity. 
  At 
  temperatures 
  sufficiently 
  high 
  the 
  temper- 
  

   ature 
  of 
  a 
  fluid 
  rises 
  during 
  isenkaumic 
  expansion; 
  at 
  intermediate 
  

   temperatures 
  it 
  falls; 
  while 
  at 
  still 
  lower 
  temperatures 
  it 
  again 
  rises, 
  

   except 
  at 
  pressures 
  above 
  a 
  certain 
  limit, 
  under 
  which 
  conditions 
  the 
  

   change 
  is 
  always 
  a 
  rise.^ 
  At 
  moderate 
  pressures 
  there 
  are 
  thus 
  two 
  

  

  inversion 
  points 
  where 
  (— 
  — 
  I 
  changes 
  sign. 
  One 
  is 
  somewhere 
  

  

  near 
  the 
  ordinary 
  boiling-point, 
  while 
  the 
  other 
  is 
  at 
  a 
  temperature 
  

   several 
  times 
  the 
  critical 
  temperature. 
  

  

  Since 
  the 
  (3p 
  and 
  ap 
  terms 
  in 
  equation 
  (2) 
  are 
  small 
  for 
  liquids 
  

  

  except 
  at 
  high 
  pressures 
  ( 
  — 
  — 
  1 
  and 
  I 
  — 
  — 
  ) 
  for 
  ordinary 
  liquids 
  

  

  are 
  practically 
  identical 
  at 
  low 
  or 
  moderate 
  pressures. 
  It 
  is 
  hardly 
  

   necessary 
  to 
  point 
  out 
  that 
  for 
  an 
  ideal 
  gas 
  aT 
  = 
  0p 
  = 
  v, 
  and 
  hence 
  

   for 
  an 
  ideal 
  gas 
  the 
  right-hand 
  members 
  of 
  equations 
  (2) 
  and 
  (3) 
  

   reduce 
  to 
  zero. 
  For 
  ordinary 
  solids 
  and 
  liquids 
  v 
  is 
  much 
  greater 
  

  

  than 
  a 
  T; 
  therefore 
  —I 
  J 
  is 
  practically 
  equal 
  to 
  — 
  . 
  Thus, 
  

  

  \ 
  dp 
  JH 
  Cp 
  

  

  the 
  heating 
  effect 
  when 
  such 
  materials 
  are 
  expanded 
  isenkaumically 
  

   is 
  nearly 
  equal 
  to 
  the 
  thermal 
  equivalent 
  of 
  the 
  work 
  done 
  {v6.p) 
  in 
  

   forcing 
  the 
  material 
  through 
  the 
  porous 
  plug 
  or 
  throttle 
  — 
  more 
  ap- 
  

   proximately 
  the 
  total 
  heating 
  effect 
  is 
  the 
  algebraic 
  sum 
  of 
  this 
  thermal 
  

   equivalent 
  of 
  the 
  net 
  work 
  done 
  on 
  the 
  substance, 
  and 
  of 
  the 
  cooling 
  

   effect 
  accompanying 
  isentropic 
  expansion, 
  the 
  latter 
  being 
  com- 
  

   paratively 
  small 
  for 
  all 
  solids 
  and 
  liquids. 
  For 
  these 
  materials, 
  

  

  ' 
  Cf. 
  P. 
  W. 
  Bridgman. 
  Proc. 
  Am. 
  Acad. 
  Sci. 
  48: 
  348. 
  1912. 
  

  

  ^ 
  Cf. 
  W. 
  McC. 
  Lewis. 
  System 
  of 
  Physical 
  Chemistry, 
  Vol. 
  II, 
  p. 
  71. 
  London, 
  1920. 
  

  

  