﻿NOV. 
  4, 
  1922 
  ADAMS: 
  temperature 
  changes 
  409 
  

  

  The 
  equations 
  given 
  for 
  the 
  three 
  types 
  of 
  adiabatic 
  expansion 
  apply 
  

   strictly 
  only 
  when 
  the 
  pressure 
  on 
  the 
  substance 
  is 
  purely 
  hydro- 
  

   static, 
  i. 
  e., 
  equal 
  in 
  all 
  directions. 
  This 
  limits 
  the 
  rigorous 
  application 
  

   of 
  such 
  formulas, 
  particularly 
  (2) 
  and 
  (3), 
  to 
  liquids 
  and 
  gases; 
  but 
  if 
  

   the 
  pressure 
  on 
  a 
  solid 
  be 
  many 
  times 
  the 
  strength 
  of 
  the 
  material, 
  

   the 
  pressure 
  may 
  be 
  nearly 
  equal 
  in 
  all 
  directions, 
  and 
  the 
  equations 
  

   may 
  then 
  be 
  used 
  for 
  calculating 
  the 
  piezo-thermal 
  effects 
  in 
  solids. 
  

   The 
  error 
  involved 
  will 
  naturally 
  be 
  smaller, 
  the 
  larger 
  the 
  pressure. 
  

   For 
  example, 
  when 
  a 
  metal 
  is 
  extruded 
  through 
  a 
  die 
  by 
  a 
  pressure 
  

   of 
  many 
  thousands 
  of 
  atmospheres, 
  the 
  rise 
  in 
  temperature 
  can 
  be 
  

   estimated 
  from 
  equation 
  (3) 
  and 
  the 
  known 
  properties 
  of 
  the 
  metal. 
  

  

  The 
  temperature 
  effects 
  for 
  the 
  three 
  kinds 
  of 
  expansion 
  and 
  

   for 
  a 
  number 
  of 
  typical 
  substances 
  are 
  shown 
  in 
  the 
  following 
  

   table. 
  

  

  Numerical 
  Value 
  of 
  Temperature 
  Rise 
  for 
  the 
  Three 
  Kinds 
  of 
  Expansion. 
  —dT/dp 
  

   IS 
  THE 
  Rise, 
  in 
  Degree 
  Centigrade 
  per 
  Megabar 
  Fall 
  in 
  Pressure 
  

  

  dT/i>p 
  

  

  In 
  making 
  calculations 
  with 
  equations 
  (1), 
  (2) 
  and 
  (3) 
  it 
  is 
  con- 
  

   venient 
  to 
  take 
  V 
  in 
  cubic 
  centimeters 
  per 
  gram, 
  p 
  in 
  megabars 
  (1 
  

   megabar 
  = 
  0.9869 
  atmosphere 
  at 
  latitude 
  40°), 
  and 
  Cp 
  in 
  deci- 
  joules 
  

   per 
  gram 
  per 
  degree 
  (1 
  calorie 
  = 
  41.84 
  deci- 
  joules). 
  An 
  alternative 
  

   way 
  is 
  to 
  take 
  p 
  in 
  kilograms 
  per 
  square 
  centimeter, 
  and 
  Cp 
  in 
  kilo- 
  

   gram-centimeters 
  per 
  gram 
  per 
  degree. 
  

  

  The 
  values 
  of 
  ( 
  :r- 
  ) 
  for 
  nitrogen 
  and 
  hydrogen 
  in 
  the 
  above 
  

   \op/H 
  

  

  table 
  were 
  not 
  calculated 
  from 
  equation 
  (3), 
  but 
  are 
  the 
  results 
  of 
  

  

  direct 
  measurements 
  of 
  this, 
  the 
  Joule-Thomson 
  effect. 
  Likewise 
  it 
  

  

  /dT\ 
  

   was 
  more 
  convenient 
  to 
  calculate 
  (t~ 
  ) 
  for 
  these 
  gases 
  from 
  the 
  

  

  relation 
  : 
  

  

  \PpJe 
  C, 
  

  

  which 
  holds 
  with 
  sufficient 
  accuracy 
  for 
  gases. 
  In 
  this 
  equation 
  n 
  

  

  