Page 44 - Battery Reference Book

Thermodynamic calculation of the capacity of a battery 1/29
Table 1.7 Heat content changes in the lead-acid cell as a function of cell temperature, temperature coefficient of emf. and acid
concentration
% &SO4 E (VI (dEldT)p T (dEldT), AH = 46191(T(dE/dT), - E)cal
(wiw) -
15°C 25°C 40°C 15-292 25-40°C 15-40°C 288K 298K 313K 288K 298K 313K
0.097 1,9043 1.8999 1.8934 0.00044 0.00043 0.00043 0.1267 0.1281 0.1346 -82109 -81795 -81 241
0.196 1.'9172 1.9133 1.9074 0.00039 0.00039 0.00039 0.1123 0.1162 0.1221 -83 370 -83010 -82465
0.487 1,9333 1.9299 1.9249 0.00034 0.00033 0.00034 0.0950 0.0983 0.1064 -84913 -84603 -83998
0.970 1.9446 1.9417 1.9372 0.00029 0.00030 0.00030 0.0864 0.0894 0.0939 -85 832 -85559 -85 144
1.92 1.9556 1.9530 1.9491 0.00026 0.00026 0.00026 0.0759 0.0775 0.0814 -86825 -86631 -86271
4.67 1.9706 1.9685 1.9654 0.00021 0.00020 0.00021 0.0576 0.0626 0.0657 -88363 -88035 -87749
8.92 1.9835 1.9819 1.9794 0.000 16 0,000 17 0.000 16 0.0490 0.0507 0.0501 -89356 -89204 -89 I16
16.39 2.0002 1.9992 1.9976 0,000 10 0,000 11 0.000 10 0.0289 0.0328 0.0313 -91 056 -90 830 -90825
21 2.0100 2.0093 2.0082 0.00070 0.00070 0.00070 0.0201 0.0209 0.0219 -91 915 -91 846 -91 749
22.72 2.0133 2.0127 2.0118 0.00060 0.00060 0.00060 0.0173 0.0179 0.0188 -92 197 -92 142 -92058
28.16 2.0254 2.0253 2.0250 0.00001 0.00002 0.00002 0.0029 0.0060 0.0062 -93 421 -93 273 -93 250
29 2.0263 2.0262 2.0260 0,00001 0,00001 0.00001 0.0029 0.0029 0.0031 -93463 -93458 -93440
32.88 2.0308 2.0308 2.0308 0.00000 0,00000 0.00000 0.0000 0.0000 0.0000 -93805 -93 805 -93 805

92 1 [ electrochemically, n can be found from Equation 1.20,
as follows:
97 I / i

i.e.
4.18AH
u/ n=

(1.75)

1.15 Thermodynamic calculation of
the capacity of a battery

In the reaction in which 1 mol of lead and lead dioxide
react with 2 mol of sulphuric acid to produce 2 mol of
79 4 , , , 1 , , , , , ! , , lead sulphate and 2mol of water (Le. the discharge
1.90 1.92 1.94 1.96 1.98 2.00 2.02 process in a lead-acid battery):
Electromotive force at 25 "C Pb + PbOz + 2HzS04 + 2e = 2PbS04 + 2820
Figure 1.11 Lead-acid battery. Relationship between cell e.m.f. the amount of electrical current produced is 2 F, Le.
and heat cont'ent change (AH) at 25°C
193 000 C and the heat content change in the reaction,
AN, is approximately -90 500 cal.
or If the initial concentration of sulphuric acid in the
B+ne=Bn- battery is 29% by weight and the final concentration at
the end of discharge is 21% by weight, the cell e.m.f.
The number of equivalents of chemical action or the values are (at 25°C) respectively 2.0262 and 2.0093 V,
number of electrons involved in the reaction is denoted and the temperature coefficients at these e.m.f. values
by n (Le. n x F = n x 96500amp-seconds). If the are 0.000010 and 0.000070 (Table 1.6).
heat content change (AH) of this cell reaction is In the above reaction 2mol (196g) of sulphuric
determined by calorimetry and the e.m.f. (E) and tem- acid are consumed, thus reducing the volume of elec-
perature coefficient of e.m.f. (dEldT) are determined trolyte by 196L.8305 = 107.07ml (the relative density