﻿MECHANICAL 
  ACTION 
  OF 
  HEAT. 
  169 
  

  

  Roche 
  and 
  Berard 
  made 
  experiments 
  as 
  perfect 
  gases, 
  would 
  lead 
  to 
  sensible 
  

   errors. 
  I 
  have, 
  therefore, 
  confined 
  my 
  calculations 
  for 
  the 
  present 
  to 
  oxygen, 
  

   hydrogen, 
  and 
  atmospheric 
  air. 
  

  

  (13.) 
  The 
  heat 
  produced 
  by 
  compressing 
  so 
  much 
  of 
  a 
  perfect 
  gas 
  as 
  would 
  

   occupy 
  unity 
  of 
  volume 
  under 
  the 
  pressure 
  unity, 
  at 
  the 
  temperature 
  0° 
  centigrade, 
  

  

  from 
  its 
  actual 
  volume 
  n 
  MV, 
  =p-?s 
  into 
  a 
  volume 
  which 
  is 
  less 
  in 
  a 
  given 
  ratio 
  5 
  

  

  (when 
  k 
  is 
  neglected 
  as 
  compared 
  with 
  t), 
  is 
  expressed 
  by 
  the 
  following 
  motion 
  : 
  — 
  

  

  nM 
  

  

  Q:=-^f 
  sYl 
  dV. 
  ^ 
  =-nMV 
  l 
  f 
  S 
  Vds 
  . 
  . 
  . 
  (25.) 
  

  

  being, 
  in 
  fact, 
  equal 
  to 
  the 
  mechanical 
  power 
  used 
  in 
  the 
  compression. 
  When 
  the 
  

   temperature 
  is 
  maintained 
  constant, 
  this 
  becomes 
  

  

  nMQ' 
  =-£-log 
  ...... 
  (26.) 
  

  

  which 
  is 
  obviously 
  independent 
  of 
  the 
  nature 
  of 
  the 
  gas. 
  

  

  Hence 
  equal 
  volumes 
  of 
  all 
  substances 
  in 
  the 
  state 
  of 
  perfect 
  gas, 
  at 
  the 
  same 
  

   pressure 
  and 
  at 
  equal 
  and 
  constant 
  temperatures, 
  being 
  compressed 
  by 
  the 
  same 
  

   amount, 
  disengage 
  equal 
  quantities 
  of 
  heat 
  ; 
  a 
  law 
  already 
  deduced 
  from 
  experi- 
  

   ment 
  by 
  Dulong. 
  

  

  (14.) 
  The 
  determination 
  of 
  the 
  fraction 
  N 
  affords 
  the 
  means 
  of 
  calculating 
  

   the 
  mechanical 
  or 
  absolute 
  value 
  of 
  specific 
  heat, 
  as 
  defined 
  by 
  Equation 
  1, 
  Sec- 
  

   tion 
  First. 
  The 
  data 
  for 
  atmospheric 
  air 
  being 
  taken 
  as 
  follows 
  : 
  — 
  

  

  N 
  = 
  04, 
  C 
  = 
  274°-6 
  centigrade, 
  

  

  -jcj 
  = 
  height 
  of 
  an 
  imaginary 
  column 
  of 
  air 
  of 
  uniform 
  density, 
  at 
  the 
  tempera- 
  

   ture 
  0° 
  cent., 
  whose 
  pressure 
  by 
  weight 
  on 
  a 
  given 
  base 
  is 
  equal 
  to 
  its 
  pressure 
  

   by 
  elasticity, 
  .... 
  =7990 
  metres, 
  

  

  =26214 
  feet:— 
  

   the 
  real 
  specific 
  heat 
  of 
  atmospheric 
  air, 
  or 
  the 
  depth 
  of 
  fall 
  equivalent 
  to 
  one 
  

   centigrade 
  degree 
  of 
  temperature 
  in 
  that 
  gas, 
  is 
  found 
  to 
  be 
  

  

  fc 
  = 
  _1— 
  - 
  = 
  72-74 
  metres 
  =238-66 
  feet 
  . 
  . 
  . 
  (27.) 
  

  

  CuMN 
  v 
  ' 
  

  

  The 
  apparent 
  specific 
  heat 
  of 
  atmospheric 
  air, 
  under 
  constant 
  pressure 
  

   according 
  to 
  De 
  la 
  Roche 
  and 
  Beeard, 
  is 
  equal 
  to 
  that 
  of 
  liquid 
  water 
  at 
  0° 
  

   centigrade 
  x 
  0-2669. 
  The 
  ratio 
  of 
  its 
  real 
  specific 
  heat 
  to 
  the 
  apparent 
  specific 
  

   heat 
  of 
  water 
  at 
  0° 
  centigrade, 
  is, 
  therefore, 
  

  

  •2669 
  x 
  ^ 
  = 
  -1906, 
  

   1.4 
  

  

  And, 
  consequently, 
  the 
  mechanical 
  value 
  of 
  the 
  apparent 
  specific 
  heat 
  of 
  liquid 
  

   water, 
  at 
  the 
  temperature 
  of 
  melting 
  ice, 
  is 
  

  

  