Page 513 - Advanced thermodynamics for engineers

506 CHAPTER 21 FUEL CELLS

However, the total work that could be obtained from a cell if it changed volume would be
dW ¼ zFEdn þ pdV (21.11)
thus, applying the First Law, and assuming the processes are reversible gives

dU ¼ dQ dW ¼ TdS pdV zFEdn (21.12)
and hence the electrical work output is

zFEdn ¼ dU þ pdV Tds ¼ dG ¼ G 2 G 1 (21.13)
For a cell which is spontaneously discharging G 2 < G 1 , and hence

dW ¼ dG (21.14)
The equations derived above define the operation of the Daniell cell from a macroscopic viewpoint.
It is instructive to examine the processes which occur at the three interfaces shown in Eqn (21.1).
Hence
9
Zn/Zn þþ þ 2e at zinc electrode
>
>
=
Zn þþ þ CuSO 4 /ZnSO 4 þ Cu þþ in solution (21.15)
>
>
Cu þþ þ 2e/Cu at copper electrode: ;
This means that the zinc is ‘dissolved’ by the sulfuric acid at the zinc electrode and a zinc anion
enters the solution. Meanwhile, two electrons are left on the zinc electrode (because the valency of
zinc is 2) and these are free to travel around the circuit, but cause the zinc electrode to be at a
negative potential, i.e. it is the cathode. The zinc anion reacts with the copper sulfate in solution to
form zinc sulfate and releases a copper ion which migrates to the copper electrode, where it withdraws
electrons from the electrode giving it a positive potential. Hence, the Daniell cell consists of electrons
(negative charges) travelling around the outer circuit, from the cathode to the anode, while positive
ions travel through the solution from cathode to anode. [Note: the convention for positive electric
current is in the opposite direction to the electron flow; the current is said to flow from the anode to the
cathode.] The net effect is to maintain the potential difference between the electrodes constant for any
given current: this is a state of dynamic equilibrium. It can be seen that the electrochemical cell is a
situation governed by thermodynamic equilibrium and steady state (irreversible) thermodynamics
(see Chapter 20).
The reactions defined in Eqn (21.15) resulted in electrons flowing from the zinc to the copper (this
would be defined as a current flowing from the copper (anode) to the zinc (cathode)), and the potential
on the anode would be higher than the cathode. If the cell was connected to a potential source (e.g. a
battery charger) such that the potential difference of the source was slightly higher than the cell emf
then the current flow could be reversed and the reaction would become

Cu/Cu þþ þ 2e 9
at Cu electrode >
>
=
Cu þþ þ ZnSO 4 /Zn þþ þ CuSO 4 in solution (21.16)
>
>
Zn þþ þ 2e/Zn at Zn electrode ;