In a cylic process, _______.

Options

A. `DeltaU = 0`
B. `DeltaQ = 0`
C. `W = 0`
D. Both (1) & (3)

Answer

To solve the question regarding a cyclic process in thermodynamics, we can break it down into the following steps:

### Step-by-Step Solution:

1. **Understanding Cyclic Process**:
- A cyclic process is one where a system returns to its initial state after undergoing a series of changes. This means that the initial and final states of the system are the same.

2. **Identifying State Variables**:
- In a cyclic process, since the system returns to its original state, the state variables such as pressure (P), volume (V), and temperature (T) will also return to their initial values. Therefore, we can conclude:
- \( P_{\text{initial}} = P_{\text{final}} \)
- \( V_{\text{initial}} = V_{\text{final}} \)
- \( T_{\text{initial}} = T_{\text{final}} \)

3. **Change in Internal Energy (\( \Delta U \))**:
- The change in internal energy (\( \Delta U \)) for an ideal gas is given by the formula:
\[ \Delta U = nC_V \Delta T \]
- Since the initial and final temperatures are the same in a cyclic process (\( T_{\text{initial}} = T_{\text{final}} \)), we have:
\[ \Delta T = 0 \implies \Delta U = 0 \]

4. **First Law of Thermodynamics**:
- The first law of thermodynamics states:
\[ \Delta U = Q - W \]
- Rearranging gives us:
\[ Q = \Delta U + W \]
- Since \( \Delta U = 0 \) in a cyclic process, we can simplify this to:
\[ Q = W \]

5. **Work Done (\( W \))**:
- The work done in a cyclic process is represented by the area enclosed by the path on a PV diagram. This area can be non-zero, indicating that work is done by or on the system during the process.

6. **Conclusion**:
- In a cyclic process, while the change in internal energy (\( \Delta U \)) is zero, the heat exchanged (\( Q \)) and the work done (\( W \)) can be non-zero. Therefore, we conclude that:
- \( \Delta U = 0 \)
- \( Q \neq 0 \)
- \( W \neq 0 \)

### Final Answer:
In a cyclic process, \( \Delta U = 0 \), \( Q \neq 0 \), and \( W \neq 0 \).