﻿HEAT 
  PRODUCED 
  BY 
  THE 
  COMPRESSION 
  OF 
  A 
  GAS. 
  295 
  

  

  closely 
  as 
  possible 
  at 
  the 
  same 
  temperature. 
  If 
  there 
  be 
  any 
  elevation 
  or 
  depres- 
  

   sion 
  of 
  temperature 
  of 
  the 
  fluid 
  in 
  passing 
  through 
  the 
  orifice, 
  it 
  may 
  only 
  be 
  

   after 
  passing 
  through 
  a 
  considerable 
  length 
  of 
  the 
  second 
  spiral 
  that 
  it 
  will 
  again 
  

   arrive 
  sensibly 
  at 
  the 
  temperature, 
  t, 
  and 
  the 
  spiral 
  must 
  be 
  made 
  at 
  least 
  so 
  long 
  

   that 
  the 
  fluid 
  issuing 
  from 
  the 
  open 
  end 
  of 
  it, 
  when 
  accurately 
  tested, 
  may 
  be 
  

   found 
  not 
  to 
  differ 
  appreciably 
  from 
  the 
  primitive 
  temperature, 
  t. 
  

  

  14. 
  Let 
  H 
  be 
  the 
  total 
  quantity 
  of 
  heat 
  emitted 
  from 
  the 
  portion 
  of 
  the 
  tube 
  

   containing 
  the 
  orifice, 
  and 
  the 
  second 
  spiral, 
  during 
  the 
  passage 
  of 
  a 
  volume 
  u 
  

   through 
  the 
  first 
  spiral, 
  or 
  of 
  an 
  equivalent 
  volume 
  u 
  through 
  the 
  parts 
  of 
  the 
  

   second 
  where 
  the 
  temperature 
  is 
  sensibly 
  t. 
  This 
  will 
  consist 
  of 
  two 
  parts 
  ; 
  one 
  

   (positive) 
  the 
  heat 
  produced 
  by 
  the 
  fluid 
  friction, 
  and 
  the 
  other 
  (negative) 
  the 
  

   heat 
  emitted 
  by 
  that 
  portion 
  of 
  the 
  fluid 
  which 
  passes 
  from 
  one 
  side 
  to 
  the 
  other 
  

   of 
  the 
  orifice, 
  in 
  virtue 
  of 
  its 
  expansion. 
  To 
  find 
  these 
  two 
  parts, 
  let 
  us 
  first 
  sup- 
  

   pose 
  the 
  transference 
  of 
  the 
  fluid 
  to 
  take 
  place 
  without 
  loss 
  of 
  mechanical 
  effect 
  

   in 
  fluid 
  friction, 
  as 
  it 
  would 
  do 
  if, 
  instead 
  of 
  the 
  partition 
  with 
  a 
  small 
  orifice, 
  

   there 
  were 
  substituted 
  a 
  moveable 
  piston, 
  and 
  if 
  a 
  volume 
  u 
  of 
  fluid, 
  on 
  the 
  side 
  

   where 
  the 
  pressure 
  is 
  higher 
  (p), 
  were 
  enclosed 
  between 
  that 
  and 
  another 
  piston, 
  

   and 
  allowed 
  to 
  slide 
  through 
  the 
  tube 
  till 
  the 
  second 
  piston 
  should 
  take 
  the 
  place 
  

   of 
  the 
  first, 
  and 
  to 
  expand 
  till 
  its 
  volume 
  should 
  be 
  u'. 
  If 
  we 
  adopt 
  the 
  same 
  

   notation 
  with 
  reference 
  to 
  the 
  volume, 
  v, 
  of 
  the 
  substance 
  between 
  the 
  pistons, 
  

   kept 
  at 
  a 
  constant 
  temperature, 
  t, 
  as 
  has 
  been 
  used 
  uniformly 
  in 
  this 
  and 
  the 
  

   preceding 
  paper; 
  we 
  shall 
  have, 
  for 
  the 
  quantity 
  of 
  heat 
  absorbed 
  during 
  the 
  

   motion 
  of 
  the 
  piston, 
  

  

  / 
  

  

  Mdv; 
  

  

  or, 
  by 
  the 
  second 
  fundamental 
  equation 
  of 
  the 
  theory, 
  (3) 
  of 
  § 
  21 
  of 
  the 
  pre- 
  

   ceding 
  paper, 
  

  

  1 
  r^dwj 
  

  

  - 
  I 
  — 
  r— 
  d 
  V, 
  

  

  VJ 
  u 
  dt 
  

  

  where 
  -as 
  denotes 
  the 
  actual 
  pressure 
  (intermediate 
  between 
  p 
  and 
  p) 
  of 
  the 
  sub- 
  

   stance 
  when 
  its 
  volume 
  is 
  v. 
  Again, 
  the 
  work 
  done 
  by 
  the 
  pistons 
  will 
  be 
  given 
  

   by 
  the 
  equation 
  

  

  W 
  

  

  = 
  I 
  ZJ 
  dv+pu—p' 
  u' 
  .... 
  (e). 
  

   J 
  u 
  

  

  j 
  If 
  now 
  the 
  transference 
  of 
  the 
  substance 
  from 
  the 
  one 
  portion 
  of 
  the 
  tube, 
  where 
  

   j 
  the 
  pressure 
  is 
  p, 
  to 
  the 
  other, 
  where 
  the 
  pressure 
  is 
  p, 
  take 
  place 
  through 
  a 
  

   j, 
  small 
  orifice, 
  exactly 
  that 
  amount, 
  W, 
  of 
  work 
  will 
  be 
  lost 
  as 
  external 
  mechanical 
  

   effect, 
  and 
  will 
  go 
  to 
  generate 
  thermal 
  vis 
  viva. 
  The 
  quantity 
  of 
  heat 
  thus 
  pro- 
  

   duced 
  will 
  be 
  

  

  j 
  I 
  I 
  ZJdv+pu—p'u'i. 
  

  

  