IOWA ACADEMY OF SCIENCE 
171 
If w represents the amount of heat taken up by the cell and also the amount 
radiated; then 
w = arV't — actdejdt t (17) 
Eliminating arV't in equation (16) and (16) and (17) 
acEt = acet + w + acTdejdt t 
Hence de^dt = acEt — acet — wjaTct 
And de-dt = E — e — ar-^act(T) (18) 
Before we can continue any further in finding de-^-dt, we must find the value 
of w, which represents both the radiated heat and the confined heat. The first 
step in finding w is to find the water equivalent of the battery, which is done 
in the following manner: 
Weight of jar 
Sp. H. .198 
W.E. 287.3 
Weight of carbon 
... 956.3 
“ .144 
“ 135.2 
Weight of zinc 
...1907.2 
“ .093 
“ 177.4 
Weight of porous cup.. 
. . . 565.4 
“ .206 
“ ll-O.S 
Weight of Fe<,S04 
. . . 12.39 “ 
“ 26.4 
“ 2.1 
149 
Weight of ZnS04 
. . . 25.2 
“ 26.4 
“ 4.13 
161 
Weight of H2SO, 
... 288.33 “ 
“ .269 
“ 77.69 
Weight of HNO3 
... 353.7 
“ .303 
“ 107.20 
Weight of H.O 
...2124.15 “ 
“ 1. 
“ 2124.15 
Total water equivalent 
3031.62 
The specific heat of a sulphate is 26.4 4-M where M is the molecular weight of 
the compound. 
We now have the water equivalent of the battery and the confined heat is 
the product of water equivalent and change in temperature. 
The radiation constant (a) is the next essential to determine. The battery 
was heated to a few degrees above the temperature of the room. The tempera- 
ture of the battery was now 27® and the room 23®. The temperature fell to 
25.25® in 45 minutes. Then the total amount of heat lost per hour was 
1.75x3031. 62H-.75 which is 7069 calories. Then the quantity of heat (Q) radi- 
ated, is 
Q = a(T" — T®") (19) 
where T' and T® is the temperature of the battery and room on the absolute 
scale. 
7069 = a (8001000000 — 7727000000) 
log a = 5.4115 — 10 
Now in finding the heat radiated we have a, T' and T® given and solve for Q. 
The value of w is thus figured for the five intervals of time and tabulated in 
data No. 5. 
As we have w we can now substitute in equation (16) and find de-:-dt. This 
is done and tabulated in data No. 6. 
We now have everything to make a complete calculation of the E. M. F. 
E. M. F. = E' + Tde^dt. 
The most Accurate way in determining the efficiency of a battery is to take 
the total amount of electrical work done in comparison with the total amount 
of chemical work done. . 
