The total internal energy change for a reversible isothermal cycles is

Options

A. Always 100 calories per degree
B. Always negative
C. 0
D. Always positive

Explanation

To solve the question regarding the total internal energy change for a reversible isothermal cycle, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Internal Energy**:
- Internal energy (U) is defined as the total energy contained within a system. It includes kinetic energy, potential energy, and any other forms of energy at the molecular level.

2. **Identify the Process**:
- The question specifies a reversible isothermal cycle. An isothermal process is one that occurs at a constant temperature.

3. **Recognize the Implications of Isothermal Conditions**:
- In an isothermal process, since the temperature (T) remains constant, the change in internal energy (ΔU) for an ideal gas is directly related to temperature.

4. **Apply the First Law of Thermodynamics**:
- The first law of thermodynamics states that the change in internal energy (ΔU) is equal to the heat added to the system (Q) minus the work done by the system (W):
\[ ΔU = Q - W \]
- For an isothermal process involving an ideal gas, the internal energy depends only on temperature. Since the temperature is constant, the change in internal energy is zero:
\[ ΔU = 0 \]

5. **Conclusion**:
- Therefore, for a reversible isothermal cycle, the total internal energy change is:
\[ ΔU = 0 \]

### Final Answer:
The total internal energy change for a reversible isothermal cycle is **0**.

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