Proportions  of  Air  Ref rigerating-Machines.  —  The  perfor-
mance of  a  refrigerating- ma  chine  may  be  stated  in  terms
of  the  number  of  thermal  units  withdrawn  in  a  unit  of  time,
or  in  terms  of  the  weight  of  ice  produced.  The  latent  heat  of
fusion  of  ice  may  be  taken  to  be  80  calories  or  144  b.t.tj.
PROPORTION   OF  AIR  OF   REFRIGERATING-MACHINES  399

Let  the  pressure  at  which  the  air  enters  the  compression-
cylinder  be  p^y  that  at  which  it  leaves  be  p^\  let  the  pressure  at
cut-off  in  the  expanding-cylinder  be  p^  and  that  of  the  back-
pressure in  the  same  be  Pi',  let  the  temperatures  correspond-
ing to  these  pressures  be  /j,  /„  /„  and  U,  or,  reckoned  from  the
absolute  zero,  Tj,  T,,  T^  and  T^.  With  proper  valve-gear
and  large,  short  pipes  communicating  with  the  cold-chamber
Pi  may  be  assumed  to  be  equal  to  p^  and  equal  to  the  pressure
in  that  chamber.  Also  t^  may  be  assumed  to  be  the  tempera-
ture maintained  in  the  cold-chamber,  and  /,  may  be  taken  to
be  the  temperature  of  the  air  leaving  the  cooler.  With  a  good
cut-off  mechanism  and  large  passages  p^  may  be  assumed  to
be  nearly  the  same  as  that  of  the  air  supplied  to  the  expanding-
cylinder.  Owing  to  the  resistance  to  the  passage  of  the  air
through  the  cooler  and  the  connecting  pipes  and  passages,  p^
is  considerably  less  than  p^.
It  is  essential  for  best  action  of  the  machine  that  the  expan-
sion and  compression  of  the  expanding-cylinder  shall  be  complete.
