the  Plug  Experiment. 
679 
plug  is  adiabatic  *,  I  shall  consider  a  modified  scheme,  in 
which  energy  is  supplied  to  the  gas,  during  its  passage 
through  the  plug,  at  such  a  rate  as  to  make  the  flow  iso- 
thermal t ;  and,  furthermore,  I  shall  consider  a  simplified 
form  of  Gray-Lussac's  and  Joule*  s  free  expansion  experiments, 
in  which  heat  is  supposed  to  be  supplied  or  withdrawn  during 
the  free  expansion  so  as  to  to  make  it  isothermal  %. 
The  fundamental  equations  for  these  three  experiments  are 
very  easy  to  deduce,  if  one  starts  by  having  a  clear  diagram. 
-^df- 
Let  A  (coordinates :  p,  v,  T)  represent  the  initial  state  of 
*  Objection  has  been  made  to  calling  the  now  adiabatic,  because  heat 
is  generated  mechanically  in  the  plug.  When  we  consider  that  this  heat 
is  probably  mainly,  if  not  entirely,  due  to  viscosity,  and  if  so,  is  developed 
in  the  gas  itself,  and  not  generated  in  the  solid  material  of  the  plu°-  by 
true  friction  and  then  communicated  to  the  gas,  the  objection  does  not 
seem  well  founded.  The  term  "  adiabatic  plug  experiment "  is,  at  all 
events,  a  convenient  designation  for  the  Joule-Thomson  experiment  as 
distinguished  from  the  proposed  isothermal  form. 
f  Phil.  Mag.  October  1903. 
%  At  first  sight,  it  seems  doubtful  whether  we  are  justified  in  applying 
thermodynamic  reasoning  to  an  essentially  tumultuous  process  such  as 
the  free  expansion  of  a  gas ;  for  the  use  of  the  two  laws  in  their  usual 
elementary  form  implies  that  the  system  under  consideration  has  a 
definite  temperature,  whereas  during  a  tumultuous  process,  the  o-as 
cannot  be  said  to  have  any  definite  temperature  at  all.  After  the 
tumultuous  motions  have  subsided  and  tue  gas  has  come  to  a  state  of 
internal  equilibrium,  both  mechanical  and  thermal,  it  has  again  a  definite 
temperature.  The  reasoning  by  which,  from  the  assumption  of  the 
nonexistence  of  infinite  sources  and  sinks  of  energy,  we  establish  the 
existence  of  the  internal  energy,  e,  as  a  function  of  the  instantaneous 
coordinates  of  the  system,  makes  no  assumption  regarding  the  nature  of 
the  path  by  which  any  state  of  the  system  may  be  reached  from  any 
other,  but  assumes  only  that  we  may  always,  by  some  means  or  of  her, 
make  the  system  pass  from  any  possible  state  to  any  other.  Hence  it  is 
entirely  legitimate  to  use  the  first  law — the  energy  law — in  comparing 
any  two  states,  regardless  of  the  nature  of  the  process  by  which  one  has 
actually  been  reached  from  the  other,  provided  it  be  not  in  the  nature  of 
things  impossible  to  make  the  system  pass  again  by  some  path  or  other 
from  the  final  to  the  initial  state. 
