The expression `[ Delta E//Delta T]_(V)` represent

Options

A. Heat capacity at constant volume
B. Heat capacity at constant at constant pressure
C. Enthalpy change
D. Eantropy change

Answer

To solve the question, we need to analyze the expression \(\left[\frac{\Delta E}{\Delta T}\right]_{V}\).

### Step-by-Step Solution:

1. **Understanding the Expression**:
The expression \(\left[\frac{\Delta E}{\Delta T}\right]_{V}\) represents the change in energy (\(\Delta E\)) with respect to a change in temperature (\(\Delta T\)) while keeping the volume constant (indicated by the subscript \(V\)).

2. **Recognizing the Terms**:
- \(\Delta E\) is the change in internal energy of the system.
- \(\Delta T\) is the change in temperature.
- The subscript \(V\) indicates that the volume is held constant during this process.

3. **Relating to Heat Capacity**:
At constant volume, the heat added to the system (\(q\)) is equal to the change in internal energy (\(\Delta E\)). This is expressed mathematically as:
\[ q = \Delta E \]
Therefore, we can write:
\[ \left[\frac{\Delta E}{\Delta T}\right]_{V} = \left[\frac{q}{\Delta T}\right]_{V} \]

4. **Defining Heat Capacity**:
The heat capacity at constant volume (\(C_V\)) is defined as:
\[ C_V = \left[\frac{q}{\Delta T}\right]_{V} \]
This means that the expression \(\left[\frac{\Delta E}{\Delta T}\right]_{V}\) is equal to the heat capacity at constant volume.

5. **Conclusion**:
Therefore, the expression \(\left[\frac{\Delta E}{\Delta T}\right]_{V}\) represents the heat capacity at constant volume (\(C_V\)).

### Final Answer:
\[ \left[\frac{\Delta E}{\Delta T}\right]_{V} = C_V \quad \text{(Heat capacity at constant volume)} \]