The temperature coefficient of the cell is `((delE)/(delT))_(P)`. Choose the correct statements `(s)`.

Options

A. When `((delE)/(delT))_(P)=0` , then `DeltaH=-nFE`
B. When `((delE)/(delT))_(P)lt0, ` then `|nFE|gt|DeltaH|`
C. When `((delE)/(delT))_(P)gt0`, then `|nFE|lt|DeltaH|` Exothermic reaction
D. When `((delE)/(delT))_(P)=0,` then `|DeltaH|gt|nFE|` Endothermic reaction.

Explanation

To solve the question regarding the temperature coefficient of the cell, which is defined as \(\left(\frac{\Delta E}{\Delta T}\right)_{P}\), we will analyze the relationships between the Gibbs free energy (\(\Delta G\)), enthalpy (\(\Delta H\)), and the electromotive force (EMF) of the cell (\(E\)).

### Step-by-Step Solution:

1. **Understanding the Relationship**:
The Gibbs free energy change (\(\Delta G\)) for a cell reaction is given by:
\[ \Delta G = -nFE \]
where \(n\) is the number of moles of electrons transferred, \(F\) is Faraday's constant, and \(E\) is the cell potential.

2. **Using the Gibbs-Helmholtz Equation**:
The Gibbs-Helmholtz equation relates \(\Delta G\) and \(\Delta H\):
\[ \Delta G = \Delta H - T\left(\frac{\Delta G}{\Delta T}\right)_{P} \]
Rearranging gives us:
\[ \frac{\Delta G}{\Delta T} = \frac{\Delta H - \Delta G}{T} \]

3. **Substituting for \(\Delta G\)**:
Substituting \(\Delta G = -nFE\) into the equation:
\[ -nFE = \Delta H - T\left(\frac{\Delta G}{\Delta T}\right)_{P} \]

4. **Rearranging the Equation**:
Rearranging this gives:
\[ \frac{\Delta E}{\Delta T} = \frac{\Delta H + nFE}{nF} \]

5. **Analyzing the Statements**:
- **Statement 1**: If \(\frac{\Delta E}{\Delta T} = 0\), then:
\[ \Delta H + nFE = 0 \implies \Delta H = -nFE \]
This statement is **correct**.

- **Statement 2**: If \(\frac{\Delta E}{\Delta T} < 0\), then:
\[ \Delta H + nFE < 0 \implies nFE > \Delta H \]
This statement is **correct**.

- **Statement 3**: If \(\frac{\Delta E}{\Delta T} > 0\), then:
\[ \Delta H + nFE > 0 \implies \Delta H > nFE \]
This statement is **correct**.

- **Statement 4**: If \(\frac{\Delta E}{\Delta T} = 0\), then:
\[ \Delta H > nFE \]
This statement is **incorrect** because we established that \(\Delta H = -nFE\).

### Final Conclusion:
The correct statements are 1, 2, and 3. Statement 4 is incorrect.