What is the change in the internal energy of a system over one complete cycle of a cyclic process?

Answer

To determine the change in the internal energy of a system over one complete cycle of a cyclic process, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Internal Energy**:
- Internal energy is a property of a system that depends only on its current state, not on how it arrived at that state. This means it is a state function.

2. **Recall the First Law of Thermodynamics**:
- The first law of thermodynamics states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (Q) minus the work done by the system (W):
\[ \Delta U = Q - W \]

3. **Define a Cyclic Process**:
- In a cyclic process, the system returns to its initial state after completing the cycle. Therefore, the initial and final states are the same.

4. **Apply the Concept of State Functions**:
- Since internal energy is a state function, the change in internal energy for a complete cycle (where the initial state equals the final state) is:
\[ \Delta U = U_{\text{final}} - U_{\text{initial}} = 0 \]

5. **Conclude the Change in Internal Energy**:
- Therefore, for a complete cycle of a cyclic process, the change in internal energy is zero:
\[ \Delta U = 0 \]

### Final Answer:
The change in the internal energy of a system over one complete cycle of a cyclic process is zero.

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