194 -R. Clausius on the Application of the 
in expanding remains exactly at a maximum density, without 
partially precipitating, (2.) that it.obeys the laws of Mariotte 
and Gay Lussac. According to these assumptions we should 
_ have 
t 150° 125° | 100° 45° 50° 25° 
“ 1 | 188 | so0 | 923 | o57 | ga4 
z 
oes" 
eel ts) oan ae Lent |. a0 ies 
pk, 
we: 
17. It remains finally to determine also the work done during 
the change of volume. For this purpose we have generally the 
equation 
(16.) W=f| pd 
1 
Now according to equation (6) if o be regarded as constant: 
dv=d(mu) 
whence pdv=pd(mu) 
for which we may also write 
(17.) pdv=d (mup)— muha 7. 
We might put in this for must the expression given by equa- : 
tion (vit) and then execute the integration. We obtain the re- ; 
sult however at once ina rather more convenient form by the — 
following substitution. According to (v1) we have : 
dp.., ie 1 mr 
and from this by employing equation (14): 
dp 1 | 
mura T= 5 [4 (mr) + Med T}. 
Hence (17) becomes 
1 
p du=d(mup) — [a (mr) + Med 7), 
and by integrating this equation we obtain 
1 
(tx.) W=mup—m,u,p,+5[m, r,—mr+ Me(T,-T)] 
whence W may be calculated, since the quantities mr and mu 
are already known from the foregoing equations, a 
