For an isolated system, `DeltaU=0`, what will be `Delta S`?

Explanation

To solve the question "For an isolated system, if ΔU = 0, what will be ΔS?", we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of an Isolated System**:
An isolated system is one that does not exchange energy or matter with its surroundings. Therefore, any changes occurring within the system must conserve energy.

2. **Identify the Given Information**:
We are given that for the isolated system, the change in internal energy (ΔU) is equal to 0.

3. **Apply 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):
\[ \Delta U = Q - W \]
Since ΔU = 0, we have:
\[ Q = W \]
This means that any heat added to the system is exactly balanced by the work done by the system.

4. **Consider the Entropy Change (ΔS)**:
For spontaneous processes, the total entropy of an isolated system must increase. The second law of thermodynamics states that the entropy of an isolated system will either increase or remain constant; it cannot decrease.

5. **Conclusion**:
Since ΔU = 0 for the isolated system and considering spontaneous processes, we conclude that:
\[ \Delta S > 0 \]
Therefore, the change in entropy (ΔS) must be greater than zero.

### Final Answer:
For an isolated system where ΔU = 0, ΔS must be greater than 0 (ΔS > 0).

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