﻿MECHANICAL 
  ACTION 
  OF 
  HEAT. 
  177 
  

  

  this 
  determination 
  may 
  be 
  considered 
  correct 
  to 
  about 
  j^oo 
  part. 
  When 
  French 
  

   measures 
  are 
  used 
  in 
  the 
  calculation, 
  the 
  following 
  is 
  the 
  result 
  : 
  — 
  

  

  v 
  = 
  l 
  cubic 
  centimetre 
  per 
  gramme, 
  

   ^• 
  = 
  1033-3 
  grammes 
  per 
  square 
  centimetre, 
  

  

  — 
  — 
  — 
  = 
  46 
  - 
  78 
  metres 
  per 
  centigrade 
  degree, 
  

  

  = 
  15348 
  feet 
  

  

  or 
  85-27 
  feet 
  per 
  degree 
  of 
  Fahrenheit. 
  

  

  The 
  difference, 
  which 
  is 
  of 
  no 
  practical 
  importance 
  in 
  calculating 
  the 
  power 
  

   of 
  the 
  steam-engine, 
  arises 
  in 
  the 
  estimation 
  of 
  the 
  density 
  of 
  liquid 
  water. 
  

  

  (22.) 
  Unit 
  of 
  weight 
  of 
  steam 
  at 
  saturation, 
  of 
  the 
  elasticity 
  P 
  x 
  and 
  volume 
  V, 
  

   corresponding 
  to 
  the 
  absolute 
  temperature 
  t 
  x 
  , 
  being 
  cut 
  off 
  from 
  external 
  sources 
  

   of 
  heat, 
  it 
  is 
  now 
  to 
  be 
  investigated 
  what 
  amount 
  of 
  power 
  it 
  will 
  produce 
  in 
  

   expanding 
  to 
  a 
  lower 
  pressure 
  P 
  2 
  and 
  temperature 
  t 
  2 
  . 
  

  

  It 
  has 
  already 
  been 
  shewn, 
  at 
  the 
  end 
  of 
  the 
  second 
  section, 
  that 
  if 
  vapour 
  at 
  

   saturation 
  is 
  allowed 
  to 
  expand, 
  it 
  requires 
  a 
  supply 
  of 
  heat 
  from 
  without 
  to 
  main- 
  

   tain 
  it 
  at 
  the 
  temperature 
  of 
  saturation, 
  otherwise 
  a 
  portion 
  of 
  it 
  must 
  be 
  liquefied 
  

   to 
  supply 
  the 
  heat 
  required 
  to 
  expand 
  the 
  rest. 
  Hence, 
  when 
  unity 
  of 
  weight 
  of 
  

   steam 
  at 
  saturation, 
  at 
  the 
  pressure 
  P 
  x 
  and 
  volume 
  V 
  l5 
  expands 
  to 
  a 
  lower 
  pressure 
  

   P, 
  being 
  cut 
  off 
  from 
  external 
  sources 
  of 
  heat, 
  it 
  will 
  not 
  occupy 
  the 
  entire 
  volume 
  

   V 
  corresponding 
  to 
  that 
  pressure, 
  according 
  to 
  Equation 
  (38.), 
  but 
  a 
  less 
  volume 
  

  

  S=mV, 
  

  

  where 
  m 
  represents 
  the 
  weight 
  of 
  water 
  remaining 
  in 
  the 
  gaseous 
  state, 
  the 
  por- 
  

   tion 
  \—m 
  having 
  been 
  liquefied 
  during 
  the 
  expansion 
  of 
  the 
  remainder. 
  The 
  

   expansive 
  action 
  of 
  the 
  steam 
  will 
  therefore 
  be 
  represented 
  by 
  

  

  /, 
  

  

  S 
  ' 
  2 
  d 
  S 
  . 
  P 
  . 
  . 
  . 
  (42.) 
  

   V 
  1 
  

  

  The 
  law 
  of 
  variation 
  of 
  the 
  fraction 
  m 
  flows 
  from 
  the 
  following 
  considera- 
  

   tions 
  : 
  — 
  

  

  Let 
  8 
  m 
  represent 
  the 
  indefinitely 
  small 
  variation 
  of 
  m 
  corresponding 
  to 
  the 
  

   indefinitely 
  small 
  change 
  of 
  temperature 
  8 
  r 
  ; 
  L, 
  the 
  latent 
  heat 
  of 
  evaporation 
  of 
  

   unity 
  of 
  weight 
  ; 
  K 
  s 
  , 
  as 
  in 
  Equation 
  (30.), 
  the 
  specific 
  heat 
  of 
  vapour 
  at 
  satura- 
  

   tion, 
  which 
  is 
  a 
  negative 
  coefficient 
  varying 
  with 
  the 
  temperature 
  ; 
  then 
  we 
  must 
  

   have 
  

  

  -L^ffl 
  = 
  mK 
  s 
  ^T, 
  or 
  — 
  = 
  — 
  -^ 
  d 
  r, 
  

  

  m 
  L 
  

  

  in 
  order 
  that 
  the 
  heat 
  produced 
  by 
  the 
  liquefaction 
  of 
  8 
  m 
  may 
  be 
  equal 
  to 
  the 
  

   heat 
  required 
  to 
  expand 
  m. 
  Hence 
  making, 
  according 
  to 
  Equation 
  (30.) 
  — 
  

  

  K 
  s 
  £T 
  = 
  fc(<5T 
  + 
  N^<5V) 
  

  

  