The efficiency of a fuel cell is given by:

Options

A. `(Delta S)/(Delta G)`
B. `(Delta H)/(Delta G)`
C. `(Delta G)/(Delta S)`
D. `(DeltaG)/(Delta H)`

Answer

To determine the efficiency of a fuel cell, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Fuel Cells**:
- A fuel cell is a device that converts chemical energy directly into electrical energy through electrochemical reactions. It typically involves the reaction of hydrogen and oxygen to produce water and electricity.

2. **Key Terms**:
- **ΔG (Gibbs Free Energy)**: This represents the maximum reversible work that can be performed by a thermodynamic system at constant temperature and pressure.
- **ΔH (Change in Enthalpy)**: This represents the total heat content of the system, which includes internal energy and the energy required to displace its environment.

3. **Efficiency Formula**:
- The efficiency of a fuel cell can be expressed in terms of Gibbs free energy and enthalpy. The formula is given by:
\[ \text{Efficiency} = \frac{\Delta G}{\Delta H} \times 100 \]

4. **Identifying the Correct Option**:
- From the options provided, we need to identify which one matches our derived formula for efficiency. The options were:
1. ΔS / ΔG
2. ΔH / ΔG
3. ΔG / ΔS
4. ΔG / ΔH
- The correct option that matches our derived formula is **Option 4: ΔG / ΔH**.

5. **Conclusion**:
- Therefore, the efficiency of a fuel cell is given by the ratio of Gibbs free energy change to the change in enthalpy, expressed as:
\[ \text{Efficiency} = \frac{\Delta G}{\Delta H} \times 100 \]