Topic 5 of 7
Batteries and fuel cells
Compare voltage, useful energy, mass and size.
A-Level 9476 (2026-2027)
Compare useful energy, size and mass
A higher voltage can help, but it does not measure capacity by itself.
A cell converts chemical free energy into electrical energy. A rechargeable battery stores reactants internally and uses an external supply to restore them during charging. A fuel cell can operate while fuel and oxidant are supplied continuously and products are removed. Hydrogen-oxygen fuel cells and improved batteries offer possible gains in compactness, lower mass and cell voltage; compare the complete system, not just an attractive electrode reaction.
| Location | Half-equation and role |
|---|---|
| Anode | 2H2(g) → 4H+(aq) + 4e-. Hydrogen is oxidised. |
| Cathode | O2(g) + 4H+(aq) + 4e- → 2H2O(l). Oxygen is reduced. |
| Overall | 2H2(g) + O2(g) → 2H2O(l). Electrons travel through the external circuit. |
The ideal standard voltage for this acidic cell is 1.23 - 0.00 = 1.23 V at 298 K; doubling its chemical equation does not give twice the voltage. Real operating voltage is lower because current flow involves losses. Several cells in series add their voltages. The fuel cell produces water at use, but hydrogen production, storage and transport affect the wider environmental and mass comparison.
| Design gain | Why it can matter in an electric vehicle | What else must be checked |
|---|---|---|
| Higher energy per unit mass | Less battery mass for the same stored energy, or more range for a given mass. | The full pack includes casing, cooling and control systems. |
| Higher energy per unit volume | A smaller pack can store the same energy. | Smaller size alone does not establish useful capacity. |
| Higher cell voltage | More energy can be delivered for the same charge; fewer series cells may meet a target voltage. | Capacity, power output, lifetime and practical operating voltage still matter. |
Worked example
Compare two hypothetical cells on a fair basis
Cell A delivers 3.2 V with capacity 2.0 Ah and mass 50 g. Cell B delivers 3.6 V with the same capacity and mass 40 g. Compare approximate stored energy per mass, ignoring voltage variation during discharge.
- Energy in Wh is voltage × capacity in Ah. A: 3.2 × 2.0 = 6.4 Wh; B: 3.6 × 2.0 = 7.2 Wh.
- Convert mass to kg: A = 0.050 kg; B = 0.040 kg.
- A: 6.4/0.050 = 128 Wh kg-1. B: 7.2/0.040 = 180 Wh kg-1.
B has higher energy per mass in this supplied comparison. These are illustrative data, not specifications of a current commercial battery.