LVI
water we mix the substance to be investigated, having ascertain-
ed before its quantity and temperature, and observe the rise of
temperature in the water.
If the quantity of water is = m, its temperature = t°, the
water represents m.t thermal units; if the specific heat of the
body in question would be the same as that of water and m1
its quantity t1, its temperature, it would contain m1. t1 thermal
units; but if we call the specific heat in question c1 the second
body contains c1. m1. t1 thermal units.Hence before the mixture
takes plases both substances contain m. t + c1. m1. t1 thermal
units. After the mixture the temperature of both bodies is uni-
form and we call it T°. Water contains m T the second body
c1 m1 T thermal units, hence both together m T + c1 m1 Tor (m
+ c1 m1) T. As by the mixture the quantity of heat is not chang-
ed, we get the following equation.
m t + c1 m1 t1 = (m + c1 m1) T
from which the value of c1 easily may be derived; f.e. an iron
ball of 2 lbs. and 93° heat is thrown into 9 lb of water at 10° and
the temperature of the water increases to 12°, find the speci-
fic heat of iron. m1 = 9, t1 = 10, m1 = 2, t1 = 93 and T = 12.
9. 10 + c1.2.93 = (9 + c1 2) 12
90 + 186 c1 = 108 + 24 c1
c1 = 1/9
Remark. 1. For finding the specific heat of bodies soluble in water,
we take another liquid, the specific heat of which we know already.
Remark. 2. The specific heat of simple bodies (elements) is inverse-
ly as the weight of their atoms (Dulong, Petit).
Thus for instance more heat is wanted for raising the tempera
ture of water than that of oil; iron wants more than zinc,
water more than earth. 290.
