﻿34 
  

  

  P. 
  de 
  Saussure 
  — 
  Graphical 
  Thermodynamics. 
  

  

  tangent 
  

  

  to 
  the 
  isothermal 
  passing 
  

  

  shows 
  that 
  MP 
  is 
  the 
  

   through 
  M. 
  

  

  AQ 
  

  

  5th. 
  From 
  P 
  to 
  Q, 
  the 
  quotient 
  — 
  — 
  becomes 
  negative 
  and 
  

  

  is 
  decreasing, 
  i. 
  e., 
  dR 
  and 
  d 
  T 
  have 
  opposite 
  signs. 
  

   6th. 
  When 
  MA 
  coincides 
  with 
  MQ 
  : 
  

   r 
  "AQ__O 
  r 
  

   K 
  ap' 
  " 
  PQ 
  

  

  = 
  

  

  

  whence 
  : 
  y 
  = 
  j^= 
  or 
  dK 
  = 
  0. 
  Hence 
  MQ 
  is 
  the 
  tangent 
  to 
  

  

  the 
  adiabatic 
  passing 
  through 
  M. 
  

  

  AQ 
  

  

  7th. 
  Above 
  point 
  Q, 
  ^^r 
  is 
  again 
  positive 
  and 
  increases 
  

  

  from 
  zero 
  (at 
  Q) 
  to 
  one 
  (at 
  infinity). 
  

  

  Thus 
  the 
  tangents 
  MP 
  and 
  MQ 
  to 
  the 
  isothermal 
  and 
  to 
  the 
  

   adiabatic, 
  divide 
  the 
  space 
  around 
  point 
  M 
  into 
  four 
  regions. 
  

   When 
  the 
  path 
  described 
  by 
  the 
  substance 
  passes 
  from 
  one 
  of 
  

   these 
  regions 
  into 
  another, 
  a 
  change 
  of 
  sign 
  occurs 
  either 
  in 
  

   dHor 
  in 
  dT 
  ; 
  this 
  change 
  taking 
  place 
  for 
  dH 
  on 
  the 
  adia- 
  

   batic, 
  and 
  for 
  dT 
  on 
  the 
  isothermal. 
  

  

  The 
  points 
  P 
  and 
  Q 
  remain 
  stationary, 
  not 
  only 
  when 
  MA 
  

   revolves 
  around 
  point 
  .Jf 
  but 
  also 
  when 
  point 
  M 
  itself 
  moves 
  

   on 
  a 
  parallel 
  to 
  the 
  axis 
  of 
  s 
  (since 
  the 
  position 
  of 
  P 
  and 
  Q 
  

   depends 
  only 
  on 
  the 
  ordinate 
  <p 
  of 
  point 
  M). 
  Hence 
  if 
  we 
  

   trace 
  the 
  tangents 
  to 
  the 
  isothermal 
  and 
  to 
  the 
  adiabatic 
  at 
  each 
  

   point 
  of 
  this 
  parallel, 
  these 
  tangents 
  will 
  form 
  two 
  pencils 
  con- 
  

   verging 
  respectively 
  at 
  P 
  and 
  at 
  Q. 
  For 
  the 
  same 
  reason, 
  if 
  

   we 
  draw 
  the 
  tangents 
  to 
  the 
  carve 
  of 
  constant 
  pressure 
  or 
  of 
  

   constant 
  volume, 
  at 
  two 
  different 
  points 
  on 
  this 
  parallel, 
  these 
  

   two 
  tangents 
  shall 
  intersect 
  each 
  other 
  on 
  the 
  axis 
  of 
  <p 
  (pro- 
  

   vided 
  however 
  that 
  the 
  two 
  points 
  be 
  sufficiently 
  near 
  each 
  

   other 
  so 
  that 
  the 
  specific 
  heats 
  can 
  be 
  regarded 
  as 
  having 
  prac- 
  

   tically 
  the 
  same 
  value 
  for 
  both 
  points). 
  

  

  12. 
  We 
  have 
  seen 
  that 
  the 
  area 
  AabB 
  (fig. 
  4) 
  is 
  equal 
  to 
  the 
  

   total 
  work, 
  P, 
  absorbed 
  during 
  the 
  transformation 
  AP. 
  In 
  

   order 
  to 
  determine 
  graphically 
  the 
  value 
  

   of 
  the 
  external 
  work 
  T 
  and 
  that 
  of 
  the 
  

   internal 
  work 
  7", 
  trace 
  the 
  curve 
  of 
  con- 
  

   stant 
  volume 
  AC 
  and 
  also 
  the 
  curve 
  PC 
  

   along 
  which 
  the 
  internal 
  work 
  dl 
  = 
  0. 
  

   These 
  curves 
  intersect 
  at 
  C 
  and 
  the 
  area 
  

   AdbB 
  is 
  now 
  divided 
  into 
  two 
  parts 
  : 
  the 
  

   hatched 
  part 
  ACcbB 
  being 
  equal 
  to 
  the 
  

   external 
  work 
  T, 
  while 
  the 
  remaining 
  part 
  

   AacC 
  is 
  equal 
  to 
  the 
  internal 
  work, 
  ab- 
  

   sorbed 
  by 
  the 
  substance 
  when 
  describing 
  

   the 
  path 
  AP. 
  

  

  