﻿38 
  i?. 
  de 
  Sausstcre 
  — 
  Graphical 
  Thermodynamics. 
  

  

  dP 
  1 
  . 
  +_ 
  . 
  . 
  

  

  -==± 
  — 
  , 
  k 
  being 
  constant 
  

  

  ($ 
  -L 
  A 
  

  

  <*v 
  1 
  « 
  , 
  . 
  

  

  -= 
  = 
  ± 
  =5", 
  x* 
  being 
  constant. 
  

   a 
  1 
  j5 
  

  

  The 
  various 
  physical 
  coefficients 
  can 
  now 
  be 
  expressed 
  in 
  

   terms 
  of 
  A 
  and 
  B 
  : 
  

  

  1st. 
  Coefficient 
  of 
  dilatation 
  at 
  constant 
  pressure 
  (a). 
  — 
  We 
  

  

  have 
  by 
  definition 
  : 
  

  

  1 
  dV 
  n 
  . 
  . 
  

   az=.~j. 
  -yp 
  , 
  F 
  being 
  constant 
  

  

  Hence 
  : 
  a 
  = 
  ± 
  ^,5 
  

  

  2d. 
  Coefficient 
  of 
  dilatation 
  at 
  constant 
  volume 
  (/9). 
  — 
  Again, 
  

  

  by 
  definition 
  : 
  

  

  1 
  tfP 
  T 
  ^ 
  . 
  . 
  

   p 
  z=z 
  — 
  -j= 
  , 
  V 
  being 
  constant. 
  

  

  Whence: 
  /3=±=— 
  

  

  3d. 
  Coefficient 
  of 
  compressibility 
  at 
  constant 
  temperature 
  (jjl). 
  

   — 
  By 
  definition 
  : 
  

  

  1 
  dY 
  

  

  //=— 
  — 
  -, 
  T 
  being 
  constant. 
  

  

  Whence: 
  // 
  = 
  =£==- 
  — 
  

  

  V 
  .D 
  

  

  4th. 
  /Specific 
  heat 
  at 
  constant 
  pressure 
  (C). 
  — 
  We 
  have 
  found 
  : 
  

  

  — 
  — 
  = 
  — 
  — 
  , 
  the 
  quotient 
  — 
  — 
  being 
  here 
  defined 
  by 
  the 
  con- 
  

  

  K 
  sdy 
  + 
  cpds 
  ' 
  ^ 
  ds 
  b 
  J 
  

  

  dition 
  : 
  P 
  = 
  constant, 
  or 
  : 
  

  

  yn 
  dP 
  7 
  dP 
  _ 
  n 
  

  

  dP 
  — 
  —dy 
  +—ds=zO 
  

  

  dcp 
  as 
  

  

  By 
  combining 
  these 
  two 
  equations, 
  we 
  shall 
  obtain 
  : 
  

  

  5th. 
  Specific 
  heat 
  at 
  constant 
  volume 
  (c). 
  — 
  Similar 
  equations 
  

   lead 
  to 
  the 
  similar 
  result 
  : 
  

  

  ~ 
  <P 
  dV 
  

  

  C 
  — 
  K 
  = 
  +^-r 
  -r— 
  

  

  ~EA 
  dq> 
  

  

  Remark 
  : 
  Subtracting 
  this 
  equation 
  from 
  the 
  preceding 
  one, 
  it 
  

   gives 
  : 
  

  

  T 
  1 
  

   C 
  - 
  C=± 
  EAB 
  

   6th. 
  Latent 
  heat 
  of 
  dilatation 
  (I) 
  : 
  

   TdT__ 
  T^ 
  

   KdT 
  —± 
  EA 
  

  

  