﻿184 
  MR 
  W. 
  J. 
  M. 
  RANKINE 
  ON 
  THE 
  

  

  To 
  obtain 
  the 
  maximum 
  gross 
  effect, 
  the 
  steam 
  must 
  continue 
  to 
  act 
  expan- 
  

   sively 
  until 
  it 
  reaches 
  the 
  pressure 
  of 
  condensation, 
  so 
  that 
  P 
  2 
  = 
  P 
  3 
  . 
  The 
  clear- 
  

   ance 
  must 
  also 
  be 
  null, 
  or 
  c=0. 
  Making 
  those 
  substitutions 
  in 
  the 
  formula 
  (47.), 
  

   we 
  find, 
  for 
  the 
  maximum 
  gross 
  effect 
  of 
  unity 
  of 
  weight 
  of 
  water, 
  evaporated 
  

   under 
  the 
  pressure 
  Pj 
  and 
  liquefied 
  under 
  the 
  pressure 
  P 
  2 
  , 
  

  

  i 
  ( 
  ,o 
  *-®T 
  

  

  In 
  order 
  to 
  calculate 
  directly 
  the 
  heat 
  which 
  is 
  converted 
  into 
  power 
  in 
  this 
  

   operation, 
  let 
  r 
  v 
  r 
  a 
  , 
  respectively 
  represent 
  the 
  absolute 
  temperatures 
  of 
  evapora- 
  

   tion 
  and 
  liquefaction, 
  and 
  L 
  , 
  the 
  latent 
  heat 
  of 
  evaporation 
  at 
  the 
  lower 
  tempera- 
  

   ture 
  t 
  2 
  ; 
  then 
  the 
  total 
  heat 
  of 
  evaporation 
  at 
  t,, 
  starting 
  from 
  t 
  3 
  as 
  the 
  fixed 
  

   point, 
  by 
  Equation 
  (33.), 
  is 
  

  

  H„, 
  !=*!<, 
  + 
  -305 
  KwCtj-t,). 
  

  

  This 
  is 
  the 
  heat 
  communicated 
  to 
  the 
  water 
  in 
  raising 
  it 
  from 
  t 
  2 
  to 
  r 
  l 
  and 
  evapo- 
  

   rating 
  it. 
  Now 
  a 
  weight 
  1 
  - 
  m 
  of 
  the 
  steam 
  is 
  liquefied 
  during 
  the 
  expansion 
  at 
  

   temperatures 
  varying 
  from 
  t, 
  to 
  t 
  2 
  , 
  so 
  that 
  it 
  may 
  be 
  looked 
  upon 
  as 
  forming 
  a 
  

  

  T" 
  *4- 
  *7* 
  

  

  mass 
  of 
  liquid 
  water 
  approximately 
  at 
  the 
  mean 
  temperature 
  -^-s— 
  -, 
  and 
  from 
  

   which 
  a 
  quantity 
  of 
  heat, 
  approximately 
  represented 
  by 
  

  

  must 
  be 
  abstracted, 
  to 
  reduce 
  it 
  to 
  the 
  primitive 
  temperature 
  t 
  2 
  . 
  

  

  Finally, 
  the 
  weight 
  of 
  steam 
  remaining, 
  m, 
  has 
  to 
  be 
  liquefied 
  at 
  the 
  tem- 
  

   perature 
  t 
  2 
  , 
  by 
  the 
  abstraction 
  of 
  the 
  heat 
  

  

  mL 
  2 
  . 
  

  

  The 
  difference 
  between 
  the 
  heat 
  given 
  to 
  the 
  water, 
  and 
  the 
  heat 
  abstracted 
  

   from 
  it, 
  or 
  

  

  H 
  2 
  , 
  , 
  -K 
  w 
  (1-m) 
  1 
  2 
  - 
  m 
  L, 
  

  

  = 
  (l-m) 
  L 
  2 
  + 
  K 
  w 
  ^-305-^) 
  (^-r,) 
  

  

  (56.) 
  

  

  is 
  the 
  heat 
  which 
  has 
  disappeared, 
  and 
  ought 
  to 
  agree 
  with 
  the 
  expression 
  (55.) 
  

   for 
  the 
  power 
  produced, 
  if 
  the 
  calculation 
  has 
  been 
  conducted 
  correctly. 
  

  

  As 
  a 
  first 
  example, 
  I 
  shall 
  suppose 
  unity 
  of 
  weight 
  of 
  water 
  to 
  be 
  evaporated 
  

   under 
  the 
  pressure 
  of 
  four 
  atmospheres, 
  and 
  liquefied 
  under 
  that 
  of 
  half 
  an 
  atmo- 
  

   sphere 
  ; 
  so 
  that 
  the 
  proper 
  values 
  of 
  the 
  coefficients 
  and 
  exponent 
  are 
  

  

  1 
  1 
  

  

  