If Q, E and W denote respectively the heat added, change in internal energy and the work done in a closed cycle process, then

Options

A. `W = 0`
B. `Q = W = 0`
C. `E = 0`
D. `Q = 0`

Explanation

To solve the problem, we need to analyze the concepts of heat (Q), internal energy change (E), and work done (W) in the context of a closed cyclic process.

### Step-by-Step Solution:

1. **Understanding Closed Cycle Process**:
- In a closed cycle process, a system returns to its initial state after completing the cycle. This means that all the properties of the system, including internal energy, return to their original values.

2. **Change in Internal Energy (E)**:
- The change in internal energy (E) for a closed cycle is given by the formula:
\[ E = U_{\text{final}} - U_{\text{initial}} \]
- Since the system returns to its initial state, we have:
\[ U_{\text{final}} = U_{\text{initial}} \]
- Therefore, the change in internal energy (E) is:
\[ E = U_{\text{initial}} - U_{\text{initial}} = 0 \]

3. **First Law of Thermodynamics**:
- The first law of thermodynamics states:
\[ Q = E + W \]
- Substituting the value of E into the equation, we get:
\[ Q = 0 + W \]
- This simplifies to:
\[ Q = W \]

4. **Conclusion**:
- In a closed cycle process, the heat added (Q) is equal to the work done (W), and the change in internal energy (E) is zero.

### Final Result:
- For a closed cycle process, we conclude that:
\[ E = 0, \quad Q = W \]