﻿166 
  

  

  MR 
  W. 
  J. 
  M. 
  RANKINE 
  ON 
  THE 
  

  

  Hence 
  the 
  following 
  are 
  the 
  values 
  of 
  the 
  apparent 
  specific 
  heats 
  of 
  unity 
  of 
  

   weight 
  of 
  a 
  theoretically 
  perfect 
  gas 
  under 
  different 
  circumstances 
  : 
  — 
  

   General 
  value 
  of 
  the 
  total 
  apparent 
  specific 
  heat 
  : 
  — 
  

  

  \ 
  

  

  

  CrcM 
  

   Apparent 
  specific 
  heat 
  at 
  constant 
  volume 
  :— 
  

  

  ^2\ 
  

  

  C«M 
  

  

  -*(*+»(M5) 
  

  

  Apparent 
  specific 
  heat 
  under 
  constant 
  pressure 
  

   Kp 
  ~CnMVN 
  +i 
  ~T 
  2 
  j 
  

  

  = 
  *{i 
  +N 
  (i_^)) 
  

  

  (18.) 
  

  

  / 
  

  

  The 
  ratio 
  of 
  the 
  apparent 
  specific 
  heat 
  under 
  constant 
  pressure 
  to 
  the 
  appa- 
  

   rent 
  specific 
  heat 
  at 
  constant 
  volume 
  is 
  the 
  following 
  : 
  — 
  

  

  = 
  1+N- 
  

  

  i 
  + 
  n(^:4) 
  _ 
  i 
  + 
  n(^-5) 
  

  

  (19.) 
  

  

  The 
  value 
  of 
  k 
  is 
  unknown 
  ; 
  and, 
  as 
  yet, 
  no 
  experimental 
  data 
  exist 
  from 
  

   which 
  it 
  can 
  be 
  determined. 
  I 
  have 
  found, 
  however, 
  that 
  practically, 
  results 
  of 
  

   sufficient 
  accuracy 
  are 
  obtained 
  by 
  regarding 
  k 
  as 
  so 
  small 
  in 
  comparison 
  with 
  t, 
  

  

  that 
  — 
  , 
  and 
  a 
  fortiori 
  -j, 
  may 
  be 
  neglected 
  in 
  calculation. 
  

  

  Thus 
  are 
  obtained 
  the 
  following 
  approximate 
  results, 
  for 
  perfect 
  gases, 
  and 
  

   gases 
  which 
  may 
  without 
  material 
  error 
  be 
  treated 
  as 
  perfect. 
  

  

  General 
  value 
  of 
  the 
  total 
  apparent 
  specific 
  heat 
  :— 
  

  

  1/1 
  TdV\ 
  , 
  . 
  

  

  1 
  /I 
  T<ZP\ 
  

  

  ~ 
  C 
  n 
  M 
  \N 
  Ydr) 
  

  

  Apparent 
  specific 
  heat 
  at 
  constant 
  volume 
  :- 
  

  

  1 
  

  

  dV 
  

  

  dr 
  

  

  K 
  v 
  = 
  

  

  = 
  fe 
  

  

  C«MN 
  

   being 
  equal 
  to 
  the 
  real 
  specific 
  heat. 
  

  

  Apparent 
  specific 
  heat 
  under 
  constant 
  pressure 
  :- 
  

   1 
  

  

  K 
  P 
  = 
  

  

  CnM 
  

  

  Q, 
  + 
  l)=ft(l 
  + 
  N) 
  

  

  (20.) 
  

  

  