562        Prof.  A.  W.  Porter  on  the  Inversion-Points  for 
Consequently  Cv  =  a  function  of  temperature  alone. 
U_U0=/(T)--+- 
and 
where  v0  is  conveniently  taken  as  the  volume  for  which  T 
is  zero,  viz.  b. 
Hence  for  a  van  der  Waals's  fluid  U  +pv  can  be  calculated, 
with  the  exception  of  a  part  of  it  which  is  a  function  of 
temperature  alone,  without  knowing  the  specific  heat  at 
constant  volume. 
Writing  the  above  in  terms   of  critical  volume  and  tem- 
ol/3  a 
hav 
perature,  and  adding  pv,  i.  e. 
U-U.+^l!W  =  f(^,-l+*) 
Fig 
.4. 
/ 
& 
// 
I 
// 
\ 
// 
I2 
// 
-o 
// 
8 
// 
3 
//                      / 
"S 
//                    / 
a: 
//                    / 
5 
/ 
/     //    / 
a/        yyiyap  r 
educed 
Pressure 
r 
The  quantity  on  the  right-hand  side  (i/r)  is  plotted  horizontally 
against  reduced  temperature  vertically  in  fig.  4,  and  the  fact 
is    brought    out   in    this    diagram    that  successive  constant- 
