﻿MECHANICAL 
  ACTION 
  OF 
  HEAT. 
  173 
  

  

  First, 
  Unity 
  of 
  weight 
  of 
  liquid 
  being 
  raised 
  from 
  the 
  temperature 
  t 
  to 
  the 
  

   temperature 
  Ti, 
  absorbs 
  the 
  heat, 
  

  

  K 
  L 
  &-««) 
  

   and 
  produces 
  the 
  expansive 
  power, 
  

  

  f 
  Vl 
  dv.P 
  

  

  Secondly, 
  It 
  is 
  evaporated 
  at 
  the 
  temperature 
  t 
  v 
  absorbing 
  the 
  heat 
  

  

  and 
  producing 
  the 
  expansive 
  power, 
  

  

  Thirdly, 
  The 
  vapour 
  expands, 
  at 
  saturation, 
  until 
  it 
  is 
  restored 
  to 
  the 
  origi- 
  

   nal 
  temperature 
  t. 
  In 
  this 
  process 
  it 
  absorbs 
  the 
  heat, 
  

  

  -P' 
  

  

  and 
  produces 
  the 
  expansive 
  power, 
  

  

  Fourthly, 
  It 
  is 
  liquefied 
  at 
  the 
  original 
  temperature, 
  giving 
  out 
  the 
  heat 
  

   and 
  consuming 
  the 
  compressive 
  power, 
  

  

  Po(V 
  -»o)- 
  

  

  The 
  equation 
  between 
  the 
  heat 
  which 
  has 
  disappeared, 
  and 
  the 
  expansive 
  

   power 
  which 
  has 
  been 
  produced, 
  is 
  as 
  follows 
  : 
  — 
  

  

  >T 
  V 
  T 
  . 
  K, 
  

  

  °dY.P 
  

  

  L 
  1 
  -L 
  + 
  K 
  L 
  (T 
  1 
  -T 
  )-/ 
  ,Tl 
  «iT. 
  

   =Px(V 
  1 
  -^ 
  1 
  )-P 
  (V 
  - 
  Vo 
  )+ 
  f 
  Vl 
  dv.P+ 
  C°dYF 
  

  

  •V. 
  

  

  (31.) 
  

  

  If 
  the 
  vapour 
  be 
  such 
  that 
  it 
  can 
  be 
  regarded 
  as 
  a 
  perfect 
  gas 
  without 
  sen- 
  

  

  -j- 
  for 
  K 
  s 
  , 
  and 
  of 
  rr—^ 
  

   dr 
  s 
  ' 
  C«M 
  

  

  sible 
  error, 
  the 
  substitution 
  of 
  ft 
  + 
  P 
  -=- 
  for 
  K 
  s 
  , 
  and 
  of 
  -r^ 
  =ft 
  N 
  t 
  for 
  P 
  V, 
  trans- 
  

  

  forms 
  the 
  above 
  to 
  

  

  L 
  1 
  -L 
  + 
  {K 
  L 
  -ft(l 
  + 
  N)}(T 
  1 
  -T 
  ) 
  j 
  

  

  rv, 
  p?, 
  \ 
  (32.) 
  

  

  In 
  almost 
  all 
  cases 
  which 
  occur 
  in 
  practice, 
  v 
  is 
  so 
  small 
  as 
  compared 
  with 
  V, 
  

   that 
  -Id 
  P 
  . 
  v 
  may 
  be 
  considered 
  as 
  sensibly 
  = 
  ; 
  and 
  therefore 
  (sensibly) 
  

  

  L 
  1 
  + 
  K 
  L 
  (T 
  1 
  -T 
  )=L 
  0+ 
  ft(l 
  + 
  N)(r 
  1 
  -T 
  ) 
  . 
  . 
  . 
  (33.) 
  

  

  