( 868 ) 
Since 
dit 
SD ae sens ee EN 
dere (13) 
equations (12) and (6) give the relation 
Md RD ger den en 
Cp (Ei 1 ») == S| bee (p.—P:) = - t €) (p,*-P,’) 
Pk 2pk t 
dt d 
Ty JD) Z 
=e mal re == D=) ee (14) 
Hence, if we return to the original coefficients by means of (8), 
(9), (10), A1) and (13), we obtain an expression for the heat-effect 
in terms of the virial-coefficients, and the initial and final pressures ; 
and if the expansion takes place against atmospheric pressure, this 
relation becomes 
13 
ee 
C N 
Ch — ae oe C (p,—1) i 
+ “p Pk 
fe ee |e eee 
4 de dt Vijn (p*=I) 
mmm nn mmm ———— = —— = ) mms 
2U°p; Cp Pk bi ay 
dd : AS 
3( t— —2D (LB AC UD 1-3) | 
w dt dt figs (p? 1) 4 
a ee ——— a es ek a= (ST 
SU pj” Cp Pk Py 
dy La: IS ; , ID 
20( « 25 ABe ete -8€ Jaren 50) 
ai a? at 
TEE 40s 
Tr. 
SEPA) EN 
Cp Pk 
which is the equation to be used in calculating the heat-effects. 
§ 7. As a first example I have taken hydrogen, and from equation 
(15) have caleulated the heat effects produced when hydrogen is 
expanded against atmospheric pressure under various conditions of 
initial temperature and pressure. The values of the virial-coefficients, 
specialised to fit the isotherms of KAMERLINGH ONNEs and BRAAK *) 
down to —217°C. and not yet published, were kindly placed at 
my disposal by Professor Onnes. These coefficients are 
1) H. KawertincH ONNEs and C. BRAAK: Comm. Phys. Lab. Leiden. No’s 95—101. 
