﻿44 
  R. 
  deSaussure 
  — 
  Graphical 
  Thermodynamics. 
  

  

  describe 
  the 
  closed 
  path 
  AEBD. 
  The 
  amount 
  of 
  this 
  work 
  

   can 
  be 
  easily 
  computed 
  from 
  the 
  experimental 
  data 
  and 
  the 
  

   area 
  of 
  the 
  quadrilateral 
  can 
  also 
  be 
  obtained 
  analytically 
  from 
  

   the 
  equations 
  of 
  its 
  sides 
  : 
  

  

  AE: 
  ?6— 
  KT 
  E 
  \ 
  

  

  DJB: 
  cps 
  =KTE 
  \ 
  

  

  AD: 
  (p 
  c 
  ~ 
  K 
  s 
  c 
  -' 
  K 
  =^l 
  f 
  

  

  EB: 
  <p 
  c 
  -V- 
  2K 
  =N° 
  J 
  

  

  Since 
  the 
  last 
  equation 
  involves 
  the 
  unknown 
  constant 
  IV, 
  the 
  

   area 
  of 
  the 
  quadrilateral 
  will 
  be 
  obtained 
  in 
  terms 
  of 
  JV, 
  and 
  

   by 
  equating 
  said 
  area 
  to 
  the 
  external 
  work 
  previously 
  com- 
  

   puted 
  in 
  terms 
  of 
  "Fand 
  T, 
  we 
  shall 
  obtain 
  an 
  equation 
  giving 
  

   the 
  unknown 
  constant 
  JV 
  in 
  terms 
  of 
  the 
  experimental 
  data. 
  

  

  In 
  short 
  iTcan 
  be 
  considered 
  as 
  known, 
  as 
  soon 
  as 
  the 
  vol- 
  

   ume 
  T^is 
  given, 
  so 
  that 
  the 
  two 
  equations 
  : 
  

  

  can 
  be 
  regarded 
  as 
  giving 
  the 
  value 
  of 
  the 
  coordinates 
  cp 
  and 
  

   s 
  in 
  terms 
  of 
  the 
  experimental 
  data 
  Tand 
  T. 
  These 
  equa- 
  

   tions 
  enable 
  us 
  to 
  find 
  the 
  position 
  of 
  the 
  point 
  corresponding 
  

   to 
  any 
  given 
  physical 
  state 
  of 
  the 
  substance, 
  without 
  having 
  to 
  

   know 
  its 
  thermodynamic 
  function, 
  provided 
  only 
  that 
  its 
  

   specific 
  heat 
  be 
  known. 
  

  

  The 
  equation 
  to 
  the 
  curves 
  of 
  constant 
  volume 
  can 
  also 
  be 
  

   made 
  use 
  of, 
  for 
  the 
  determination 
  of 
  the 
  thermodynamic 
  

   function 
  in 
  terms 
  of 
  <p 
  and 
  s 
  ; 
  for, 
  since 
  we 
  know 
  how 
  to 
  find 
  

   the 
  value 
  of 
  the 
  constant 
  JV 
  corresponding 
  to 
  any 
  given 
  value 
  

   of 
  the 
  volume 
  V, 
  it 
  may 
  be 
  possible 
  to 
  express 
  iv 
  in 
  terms 
  of 
  

   T^by 
  an 
  empirical 
  function: 
  1ST 
  — 
  <p 
  (V). 
  In 
  this 
  case, 
  the 
  

   general 
  equation 
  to 
  the 
  curves 
  of 
  constant 
  volume 
  can 
  be 
  

   written 
  : 
  

  

  y(V)= 
  <p 
  c-K 
  s 
  c 
  - 
  2K 
  

  

  This 
  equation 
  gives 
  V 
  in 
  terms 
  of 
  <p 
  and 
  s; 
  hence 
  it 
  is 
  one 
  of 
  

   the 
  three 
  equations 
  involved 
  in 
  the 
  thermodynamic 
  function. 
  

  

  All 
  that 
  has 
  been 
  said 
  in 
  this 
  paragraph 
  concerning 
  the 
  vol- 
  

   ume 
  V, 
  applies 
  also 
  to 
  the 
  pressure 
  P, 
  provided 
  the 
  specific 
  

   heat 
  at 
  constant 
  volume 
  c, 
  be 
  replaced 
  by 
  the 
  specific 
  heat 
  at 
  

   constant 
  pressure 
  C. 
  The 
  general 
  equations 
  to 
  the 
  curves 
  of 
  

   constant 
  pressure 
  would 
  be 
  : 
  

  

  X(P) 
  =(p 
  c 
  - 
  K 
  s 
  c 
  -* 
  K 
  

  

  (%{-P) 
  being 
  a 
  function 
  obtained 
  empirically), 
  and 
  the 
  complete 
  

   thermodynamic 
  function 
  of 
  the 
  substance 
  would 
  then 
  be 
  : 
  

   ( 
  j(P) 
  = 
  (p 
  c 
  - 
  K 
  s 
  c 
  - 
  2K 
  

  

  KTE= 
  q>s 
  

  

  