ME. OLEEK MAXWELL OX THE DYNAMICAL THEOEY OE GASES. 
79 
without exchange of heat with other bodies. We also find 
Bp_Bg ,_B0 
P ~ 9 5 
= 2±Sl’dg (108) 
3/3 P ’ [ } 
which gives the relation between the pressure and the density. 
Specific Heat of Unit of Mass at Constant Volume. 
The total energy of agitation of unit of mass is /3V 2 =E, or 
E= ^ V (109) 
If, now, additional energy in the form of heat be communicated to it without changing 
its density, 
BE= ^P = s ll (HO) 
Hence the specific heat of unit of mass of constant volume is in dynamical measure 
BE 3/3 
B0 2 §6 
( 111 ) 
Specific Heat of Unit of Mass at Constant Pressure. 
By the addition of the heat BE the temperature was raised B$ and the pressure B p. 
Now, let the gas expand without communication of heat till the pressure sinks to its 
former value, and let the final temperature be S-f-B'5. The temperature will thus sink 
by a quantity B0— B'0, such that 
Bfl-B' 2 ~dp 2 B0 
“2 + 3/3 p “2 + 3/3 6 ’ 
whence 
B'A 3/3 B A . /1]91 
0 2+3/3 0 { 
and the specific heat of unit of mass at constant pressure is 
BE 2 + 3/3 p 
B'A 2 g$ 
(113) 
The ratio of the specific heat at constant pressure to that of constant volume is known 
in several cases from experiment. We shall denote this ratio by 
v=-W> fl“) 
whence 
The specific heat of unit of volume in ordinary measure is at constant volume 
1 P 
7—1 J 0 ’ 
(115) 
( 110 ) 
