The efficiency of a fuel cell is given by: `DeltaG//DeltaS`, `DeltaG//DeltaH`, `DeltaS//DeltaG`, `DeltaH//DeltaG`

Options

A. `DeltaG//DeltaS`
B. `DeltaG//DeltaH`
C. `DeltaS//DeltaG`
D. `DeltaH//DeltaG`

Explanation

To solve the question regarding the efficiency of a fuel cell, we need to analyze the given options and understand the relevant thermodynamic concepts.

### Step-by-Step Solution:

1. **Understanding Fuel Cells**:
A fuel cell is a device that converts chemical energy from fuel directly into electrical energy through electrochemical reactions.

2. **Defining Efficiency**:
The efficiency of any energy conversion device is generally defined as the ratio of useful output energy to the total input energy. In the context of a fuel cell, we need to relate the Gibbs free energy (ΔG) and enthalpy (ΔH).

3. **Identifying Relevant Terms**:
- **ΔG (Gibbs Free Energy)**: This represents the maximum reversible work that can be performed by the system at constant temperature and pressure. It is the useful work output of the fuel cell.
- **ΔH (Enthalpy)**: This represents the total heat content of the system. It is the total energy input into the fuel cell.

4. **Formulating Efficiency**:
The efficiency (η) of the fuel cell can be expressed as:
\[ \eta = \frac{\text{Useful output energy}}{\text{Total input energy}} = \frac{\Delta G}{\Delta H} \]

5. **Conclusion**:
From the analysis, the correct expression for the efficiency of a fuel cell is:
\[ \frac{\Delta G}{\Delta H} \]

### Final Answer:
The efficiency of a fuel cell is given by \( \frac{\Delta G}{\Delta H} \).

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