216 HOLTZMANN ON THE HEAT AND ELASTICITY 
= 239400, and of this the above calculated theoretical duty of 
the low pressure engine is only the fourteenth part, and the me- 
chanical force really obtained only the twenty-eighth. 
40. The calculation of the theoretical effect of the expansion- 
engine now likewise becomes very simple. If with any pres- 
sure p, v is the volume which 1 steam occupies, ¢ the weight of 
1 cubic metre of this steam, and ¢ its temperature, then p dv 
is the duty which the steam yields on its expansion dv. This 
duty is, as in No. 3, equal 
Be LD 
With this expansion the steam retains its quantity of heat, its 
temperature sinks, and the temperature passes over into its equi- 
valent mechanical force. Since the steam retains its quantity of 
heat, we have during the expansion, 
BE) BEER TEE. Sore 
Eepaa ee a 3 | 6. 15.05 
and dp _ab dt 
== 4 a TGA 
. . 
p ke (1+at)? 
Moreover, the three quantities, p, g and ¢, are combined by the 
equation p=ke(l+ai); 
whence results ie 
Eta es 
Sar pene! > K+ at)?" is 
If we substitute in this expression 57 ap ? from the preceding, and 
lastly substitute this value of dg in "ie expression of the me- 
chanical action above calculated, we obtain, after some simple 
reductions, the mechanical force for the change of the tempera- 
the integral of which 
ture ¢ by d¢ equal 
i tak has, 
__ ab 
{ - ab 
Ler 
——.NL(1 + at)+akt + Const. 
a 
If the change of temperature commences at the temperature 
#,, and proceeds until the temperature becomes /,, then the me- 
chanical force during the expansion of 1 kilogramme of steam 
as 
