The  possible  ways  in  which  a  given  mass  of  gas  may  undergo  a
continuous  transformation,  not  involving  any  chemical  change,  are
evidently  the  following  :  (a)  at  constant  volume  by  changing  the
pressure  indirectly  through  a  change  in  the  temperature  ;  (5)  at  con-
stant pressure  by  changing  the  volume  indirectly  through  a  change
in  the  temperature  ;  ((?)  at  constant  temperature,  that  is  isothermally,
and  hence  in  accordance  with  the  relation  of  Boyle's  Law;  the  values
of  p  and  F^are  then  related  as  pV=p\V\  =  a  constant;  (<7)  without
the  addition  or  subtraction  of  heat,  that  is,  as  it  is  called,  adiabati-
cally ;  as  will  be  seen  in  Section  21  the  equation  expressing  this
relation  is  pVK=plVKl  —  ^  constant;  (e)  in  accordance  with  the
condition  that  the  intrinsic  energy  shall  be  constant,  that  is,  an
isoenergio  transformation  ;  for  a  perfect  gas  this  condition  is  evidently
equivalent  to  that  of  an  isothermal  change  ;  (/)  the  change  may  be
under  the  condition  of  constancy  in  what  is  called  the  entropy  of
the  gas,  that  is,  the  change  may  be  isentropic  ;  for  a  reversible  trans-
formation, as  will  be  discussed  in  Section  31,  this  is  equivalent  to

1  See  Edser,  "  Heat  for  Advanced  Students,"  p.  302.
FUNDAMENTAL   LAWS


17


an  adiabatic  change  ;  or  (#)  the  transformation  may  not  be  in  ac-
cord with  any  of  the  above  conditions,  in  which  case  frequently  it
may  be  represented  by  a  relation  of  the  form  pVn  =plV1n=  a  con-
stant ;  or,  it  may  be  assumed  to  take  place  in  a  series  of  infinitesi-
mal steps  which  are  in  accordance  with  some  of  the  above  conditions.
