220 IF. G. Mixter — Heat of Combustion of Hydrogen. 



(1) Suppose m grams of the mixed gases, originally in the 

 state j9, v, tj, is first cooled and expanded or compressed until 

 its state is F, v^^ 0° ; by Joule's law, the total loss of energy 

 will be mC^i^ calories, where Cv is the specific heat at constant 

 volume of the combined gases. Let the gases now combine at 

 constant pressure, giving out Q calories, in the form of heat. 



Pi' 



and receiving -^^ calories, in the form of work done by the 



outside pressure (the final volume of the water being negligible 

 in comparison with v^. The total loss of energy by this 

 process is thus 



Q- ^ + mO^t^. 



(2) In the second process, starting with the same conditions, 

 let the mixture be burned at constant volume, v, the final tem- 

 perature of the calorimeter being t ; let the observed heat be 

 Q^. If a^ is the density of steam at t and^j*! its pressure, the 

 mass of uncondensed vapor will be a^v (again neglecting the 

 volume of the water) ; let this be compressed, at constant tem- 

 perature, t, until all is condensed. The energy given to it in 



the form of work will be -~ calories, and the energy lost will 



be cTj-yLt, where L^ is the latent heat of steam at the tempera- 

 ture t. Let the resulting water be then cooled from t to 0°, 

 giving out mt calories. We now have water in the same final 

 state as by the first process, so that the losses of energy in the 

 two cases are equal. 

 Thus 



Q - ^ + mC^t^ = Q' + a,vL,- ^ + mt 



o J 



or Q = Q' + cr,vLt+ ^ +mt—7nCj^— ^. 



The product o-^Lt may be got most conveniently from the 

 formula of Clapeyron which, when we neglect the volume of 

 water in comparison with the volume of steam, becomes 



..L. = i(273 + o|, 



-^ being obtained from a table giving the pressure of steam at 



different temperatures. 



If one gram of hydrogen is burned, and P is the standard 

 pressure, 760"°^ of mercury, at latitude 45° 



Py„ '76-Xl3'6x980-6Xl6680- '^^ , . 



-^ = , ,^ , ^ — = 404- calories. 



J 4-181x10' 



