The thermodynamic efficiency of cell is given by

Options

A. `(/_\H)/(/_\G)`
B. `-(nFE)/(/_\G)`
C. `-(nEF)/(/_\H)`
D. `nFE^(@)`

Answer

To find the thermodynamic efficiency of a cell, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Thermodynamic Efficiency**:
- Thermodynamic efficiency of a cell is defined as the ratio of Gibbs energy change (ΔG) to the enthalpy change (ΔH) in the overall cell reaction.
- Mathematically, this can be expressed as:
\[ \text{Thermodynamic Efficiency} = \frac{\Delta G}{\Delta H} \]

2. **Relating Gibbs Energy Change to EMF**:
- The Gibbs energy change (ΔG) is related to the electromotive force (EMF) of the cell (E_cell) by the equation:
\[ \Delta G = -nFE_{\text{cell}} \]
- Here, \( n \) is the number of moles of electrons transferred, and \( F \) is Faraday's constant.

3. **Substituting ΔG in the Efficiency Equation**:
- We can substitute the expression for ΔG into the thermodynamic efficiency equation:
\[ \text{Thermodynamic Efficiency} = \frac{-nFE_{\text{cell}}}{\Delta H} \]

4. **Final Expression**:
- Thus, the thermodynamic efficiency of the cell can be expressed as:
\[ \text{Thermodynamic Efficiency} = -\frac{nFE_{\text{cell}}}{\Delta H} \]

5. **Conclusion**:
- The correct answer to the question regarding the thermodynamic efficiency of a cell is:
\[ -\frac{nFE_{\text{cell}}}{\Delta H} \]