Question

The efficiency of a fuel cell is given by

• A. $ΔG/ΔS $
• B. $ΔG/ΔH $
• C. $ΔS/ΔG $
• D. $ΔH/ΔG $

Answer 1

The Correct Option is B

The efficiency of a fuel cell is determined by comparing the work output of the cell, represented by the Gibbs free energy change (ΔG), to the total energy input, represented by the enthalpy change (ΔH). This can be represented by the formula for efficiency:

\text{Efficiency} = \frac{ΔG}{ΔH}

Let's explain why each option is correct or incorrect based on this concept:

1. ΔG/ΔS: This ratio does not represent efficiency. Here, ΔS indicates entropy change, which is not directly related to the efficiency calculation of a fuel cell.
2. ΔG/ΔH: This is the correct formula for the efficiency of a fuel cell. It compares the usable energy (Gibbs free energy) to the total energy content (enthalpy).
3. ΔS/ΔG: This ratio has no direct significance in calculating fuel cell efficiency. It does not involve enthalpy, which is crucial for determining efficiency.
4. ΔH/ΔG: This is the inverse of the correct efficiency formula. Instead of assessing how much of the total energy becomes useful work, this would indicate how much total energy is represented by work, which is conceptually not how efficiency is defined.

The correct answer is therefore ΔG/ΔH, as it correctly reflects the comparison between the useful energy and the total energy in the system, which is the definition of efficiency in thermodynamics.