Page 51 - Handbook of Battery Materials

1.3 Thermodynamics 17

For the temperature coefficient of the reaction free energy follows, because of
thermodynamic relations [7], by partial differentiation of Equation 1.5:
∂ G

=− S (1.17)
∂T p

∂ ε 0 1
=− · (− S) p (1.18)
∂T z · F
p
The reversible reaction heat of the cell is defined as the reaction entropy multiplied
by the temperature (Equation 1.5). For an electrochemical cell this is also called
the PELTIER effect and can be described by the difference between the reaction
enthalpy H and the reaction free energy G. If the difference between the
reaction free energy G and the reaction enthalpy H is less than zero, the cell
becomes warmer. On the other hand, for a difference greater than zero, it cools
down. The reversible heat of formation W of the electrochemical cell is therefore:
W = G − H (1.19)
W =−T · S

For the Daniell element at standard conditions, T = 298 K
Zn + CuSO 4 −→ ZnSO 4 + Cu
reaction enthalpy H =−210.1kJmol −1
−1
reaction free energy G =−208 kJ mol
Heat W = G − H
−1
W = 2.1kJ mol
The reversible amount of heat of 2.1 kJ·mol −1 is consumed by charging and
released by discharging.

The relationship between free reaction enthalpy, temperature, cell voltage, and
reversible heat in a Galvanic cell is reflected by the GIBBS–HELMHOLTZ equation
(Equation 1.20).

∂ G
H = G − T · (1.20)
∂T p
Insertion of Equation 1.8 for G results in

∂ ε 0
H = z · F · ε 00 + T · (1.21)
∂T
p
Earlier it was deduced that for S and G:

∂ ε 0
S = z · F · (1.22)
∂ T p
G =−z · F · ε 0 (1.23)