The entropy change can be calculated by using the expression `DeltaS-(q_(rev))/(T)`. When water freezes in a glass beaker, choose the correct statement amongst the following:

Options

A. `Delta S` (system) decreases but `Delta S` (surroundings) remains the same
B. `Delta S` (system) increases but `Delta S` (surroundings) decreases
C. `Delta S` (system) decreases but `Delta S` (surroundings) increases
D. `Delta S` (system) decreases but `Delta S` (surroundings) also decreases

Explanation

To solve the question regarding the entropy change when water freezes in a glass beaker, we will analyze the situation step by step.

### Step-by-Step Solution:

1. **Understanding the Process**:
- When water freezes, it undergoes a phase change from liquid to solid. During this process, the water loses heat to the surroundings.

2. **Entropy of the System**:
- The system in this case is the water. As water freezes, it becomes more ordered (solid state is more ordered than liquid state). Therefore, the randomness or disorder of the water decreases.
- This means that the entropy change for the system (ΔS_system) is negative, indicating a decrease in entropy.

3. **Entropy of the Surroundings**:
- As the water loses heat to the surroundings, the temperature of the surroundings increases. When the temperature of the surroundings increases, the randomness or disorder in the surroundings increases.
- Thus, the entropy change for the surroundings (ΔS_surrounding) is positive, indicating an increase in entropy.

4. **Total Entropy Change**:
- The total entropy change of the universe (ΔS_total) can be expressed as:
\[ ΔS_{total} = ΔS_{surrounding} + ΔS_{system} \]
- Since ΔS_system is negative and ΔS_surrounding is positive, for the total entropy change to be constant, the increase in ΔS_surrounding must be greater than the decrease in ΔS_system.

5. **Conclusion**:
- Therefore, when water freezes in a glass beaker, we conclude that:
- ΔS_system decreases (entropy of the system decreases).
- ΔS_surrounding increases (entropy of the surroundings increases).
- The correct statement is that the entropy of the system decreases while the entropy of the surroundings increases.

### Final Answer:
The correct statement is: **ΔS_system decreases and ΔS_surrounding increases.**

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