﻿MECHANICAL 
  ACTION 
  OF 
  HEAT. 
  165 
  

  

  Section 
  II. 
  — 
  Of 
  Real 
  and 
  Apparent 
  Specific 
  Heat, 
  especially 
  in 
  the 
  State 
  

  

  of 
  Perfect 
  Gas. 
  

  

  (9.) 
  The 
  apparent 
  specific 
  heat 
  of 
  a 
  given 
  substance 
  is 
  found 
  by 
  adding 
  to 
  the 
  

   real 
  specific 
  heat 
  (or 
  the 
  heat 
  which 
  retains 
  its 
  form 
  in 
  producing 
  an 
  elevation 
  of 
  

   one 
  degree 
  of 
  temperature 
  in 
  unity 
  of 
  weight) 
  that 
  additional 
  heat 
  which 
  disap- 
  

   pears 
  in 
  producing 
  changes 
  of 
  volume 
  and 
  of 
  molecular 
  arrangement, 
  and 
  which 
  

   is 
  determined 
  by 
  reversing 
  the 
  sign 
  of 
  Q 
  1 
  in 
  equation 
  6 
  of 
  Section 
  I. 
  (so 
  as 
  to 
  

   transform 
  it 
  from 
  heat 
  evolved 
  to 
  heat 
  absorbed), 
  and 
  taking 
  its 
  total 
  differential 
  

   coefficient 
  with 
  respect 
  to 
  the 
  temperature. 
  Hence, 
  denoting 
  total 
  apparent 
  spe- 
  

   cific 
  heat 
  by 
  K, 
  — 
  

  

  K 
  _dQ 
  d.q 
  1 
  _dq 
  dQi 
  dQ 
  1 
  dY 
  

  

  ~ 
  d 
  t 
  dr 
  d 
  t 
  di 
  dY 
  ' 
  d 
  t 
  

  

  1 
  r3/fcM 
  , 
  ,/dV/l 
  dV\ 
  dV\ 
  i 
  /10 
  . 
  

  

  Another 
  mode 
  of 
  expressing 
  this 
  coefficient 
  is 
  the 
  following 
  : 
  — 
  

  

  Denote 
  the 
  ratio 
  WkM 
  ^ 
  ^' 
  

  

  and 
  the 
  real 
  specific 
  heat 
  by 
  it 
  ( 
  14 
  ) 
  

  

  1 
  

  

  ~C«MN 
  

  

  Then 
  

  

  The 
  value 
  of 
  -j— 
  is 
  to 
  be 
  determined 
  from 
  the 
  conditions 
  of 
  each 
  particular 
  

  

  case 
  ; 
  so 
  that 
  each 
  substance 
  may 
  have 
  a 
  variety 
  of 
  apparent 
  specific 
  heats, 
  accord- 
  

   ing 
  to 
  the 
  manner 
  in 
  which 
  the 
  volume 
  varies 
  with 
  the 
  temperature. 
  

  

  If 
  the 
  volume 
  is 
  not 
  permitted 
  to 
  vary, 
  so 
  that 
  -5 
  — 
  = 
  0, 
  there 
  is 
  obtained 
  the 
  

  

  following 
  result, 
  being 
  the 
  apparent 
  specific 
  heat 
  at 
  constant 
  volume 
  : 
  — 
  

  

  v 
  1 
  (\ 
  . 
  .d\J\ 
  

  

  = 
  ft 
  (l-N(T-K)§IL) 
  . 
  . 
  (16.) 
  

  

  (10.) 
  When 
  the 
  substance 
  under 
  consideration 
  is 
  a 
  perfect 
  gas, 
  it 
  has 
  already 
  

   been 
  stated 
  (Eq. 
  7), 
  that 
  -5 
  — 
  = 
  — 
  T 
  , 
  -ry 
  = 
  ; 
  and 
  because 
  the 
  volume 
  of 
  unity 
  

   of 
  weight 
  is 
  directly 
  as 
  the 
  absolute 
  temperature 
  and 
  inversely 
  as 
  the 
  pressure, 
  

  

  1 
  dY 
  1 
  1 
  dV 
  

  

  V 
  dr 
  ~ 
  t 
  ~P 
  dr 
  * 
  ' 
  * 
  ^ 
  17 
  '' 
  ) 
  

  

  