a err mm pi ry Ir b 
% (toma BT [BSD — TUD + RT 
or 
a 7 ™ el rm rj b 
pie Tg [DTO] + BT. 
p=0 v v—b 
Making use of this value of 7v, we deduce from ~; = 72 the 
following formula: 
a 
pb LN edna f(T) = Tif (4)) = 
l 
Vv] 
RT, b | 
vj —b | 
= bs [2/00 TN ee 
If we want to keep a and 6 at the value which they have in 
the equation of state, in which the pressure of one atmosphere is 
chosen as the unity of pressure and the volume which the unity 
of weight of the gas occupies under that pressure and at 0° as 
unity of volume, this last formula assumes the following form: 
4 Al 2 a ‘ 7 rm i IY gif ET) 
pi) 208 [LSO AO — 
m | vj u—b| 
2 273 (4 farcny— men) |— dL 
RE be [24 (2) — 2f" (1) |— a. 
: RTD 
Let us think vo so great that the quantities dE 
Vo Wk == 
ALBA ae 
)C pV Che) may be neglected, then the cooling is 
Vo meus b v te) ? 
= 1 RTD 
determined by the value which nif rans = possess- 
Ui Dj 
es. If at given 7) we make the value of v, pass through all the 
values from v}=o to vj =b, and if we think 7, chosen in 
such a way that: 
[BSC — Af) > HO DA + anys, 
the value of the expression : 
= ery) = hee —— 
7 
Viart 
