﻿568 
  

  

  MR 
  W. 
  J. 
  M. 
  RANKINE 
  ON 
  THE 
  

  

  increase 
  of 
  total 
  heat 
  d 
  Q, 
  while 
  the 
  volume 
  remains 
  constant, 
  is 
  expressed 
  as 
  

   follows 
  : 
  — 
  

  

  §!*«=.{ 
  <j/H«V+ 
  *«>}*« 
  .... 
  (71.) 
  

  

  the 
  heat 
  Q 
  being 
  treated 
  as 
  a 
  constant 
  in 
  the 
  integration. 
  

  

  If 
  we 
  now 
  investigate 
  the 
  entire 
  quantity 
  of 
  heat, 
  both 
  sensible 
  and 
  latent, 
  

   which 
  is 
  consumed 
  by 
  a 
  body 
  during 
  a 
  simultaneous 
  small 
  change 
  of 
  total 
  heat 
  

   e?Q 
  and 
  volume 
  d 
  V, 
  we 
  find 
  the 
  following 
  results 
  : 
  — 
  

  

  Sensible 
  heat 
  (which 
  retains 
  its 
  condition) 
  . 
  . 
  . 
  . 
  - 
  a 
  Q 
  

   Latent 
  heat, 
  or 
  heat 
  which 
  disappears 
  in 
  overcoming 
  

   molecular 
  action 
  

  

  d 
  S 
  _. 
  dS 
  ~- 
  T 
  

   dQ 
  dq 
  + 
  TV 
  dY 
  

  

  PdV 
  

  

  (72.) 
  

  

  Latent 
  heat 
  equivalent 
  to 
  the 
  visible 
  mechanical 
  effect 
  

   The 
  amount 
  being 
  

  

  dq+d.S+?dY= 
  (i+dS\dQ+ 
  (~ 
  + 
  P\dY= 
  

  

  This 
  formula 
  expresses 
  completely 
  the 
  relations 
  between 
  heat, 
  molecular 
  

   action, 
  and 
  expansion, 
  in 
  all 
  those 
  cases 
  in 
  which 
  the 
  expansive 
  power 
  developed, 
  

   P 
  d 
  V, 
  is 
  entirely 
  communicated 
  to 
  the 
  bodies 
  enclosing 
  the 
  substance 
  which 
  ex- 
  

   pands. 
  

  

  (49.) 
  The 
  following 
  coefficients 
  are 
  contained 
  in, 
  or 
  deducible 
  from 
  it. 
  

  

  The 
  ratio 
  of 
  the 
  specific 
  heat 
  at 
  constant 
  volume 
  to 
  the 
  real 
  specific 
  heat 
  : 
  — 
  

  

  T 
  = 
  1 
  + 
  U 
  = 
  } 
  +( 
  lf%$- 
  dY 
  + 
  4 
  / 
  W 
  •'••'• 
  (73.) 
  

   The 
  coefficient 
  of 
  latent 
  heat 
  of 
  expansion 
  at 
  constant 
  heat 
  : 
  — 
  

  

  . 
  . 
  . 
  (74.) 
  

  

  "D 
  f\ 
  

  

  dY 
  + 
  ^ 
  = 
  H 
  dQ 
  

  

  The 
  ratio 
  of 
  the 
  specific 
  heat 
  at 
  constant 
  pressure 
  to 
  the 
  real 
  specific 
  heat 
  is 
  

   found 
  as 
  follows. 
  To 
  have 
  the 
  pressure 
  constant, 
  we 
  must 
  have 
  

  

  dV 
  

  

  l^dQ+^dV: 
  

  

  consequently 
  the 
  ratio 
  in 
  question 
  is 
  

  

  dV 
  

  

  A 
  d 
  V 
  dO 
  

  

  ; 
  • 
  or 
  — 
  = 
  -^- 
  

  

  ' 
  dq 
  dF_ 
  

  

  dV 
  

  

  Kp 
  , 
  a 
  S 
  

   f 
  — 
  1-1 
  

  

  fc 
  dq 
  

  

  6$+*) 
  

  

  dq 
  

  

  dV_ 
  

   dV 
  

  

  = 
  1 
  + 
  

  

  H 
  J 
  d&- 
  

  

  dV 
  + 
  tf>'(Q) 
  

  

  -Q 
  

  

  Uq) 
  

  

  dV 
  

  

  dV 
  

  

  (75.) 
  

  

  