Energy of Heated Water. 389 



ing value for the excess of the final volume to which the mixed 

 liquid and vapour expand above the original volume of the liquid : 



K hyp. log -L 



sr"-- ™ 



dt 2 

 in which ~~ denotes the rate at which the pressure, in lbs. on 



2 



the square foot, varies with temperature at the final temperature. 



When applied to the water in a steam-boiler, these equations 

 take the following form : — 



The value of K for liquid water is — 



772 foot-pounds per degree of Fahrenheit in a pound of 



water, or 

 1389*6 foot-pounds per Centigrade degree in a pound of 



water, or 

 423*55 kilogrammetres per Centigrade degree in a kilogramme 



of water. 

 The final absolute temperature is 212° F. + 461°*2 = 673°*2F. 



The corresponding value of ■—, for Fahrenheit's scale and 



British measures, is 42; and 772-^-42 = 18*38. 



Let T denote the initial temperature on Fahrenheit's ordinary- 

 scale, so that *j = T + 461°*2. Then 



Energy, in foot -pounds, exerted by each pound of water 



= 772{T-212°-673-3hyp.log(^p)}* i (8) 



Final volume of expansion of mixed water and steam, in cubic feet 

 per pound 



= 18-38 hyp. log ( T ~f). ... (4) 



It is worthy of remark, that the energy developed depends solely 

 on the specific heat of the substance in the liquid state, and the 

 initial and final temperatures, and not on any other physical pro- 

 perty of the substance. 



The following Table gives some results of the formulae. 



The first column contains the temperature on the ordinary 

 scale of Fahrenheit, with intervals of 36° F. =20° C. 



The second column contains the expansive energy of one 

 pound of water, in foot-pounds. 



* This agrees with the formula given by J. B. in * The Engineer ' of the 

 2nd of October 1863, page 200. 



