entropy of a system decreases

Options

A. When heat is supplied to a system at constant temperature
B. When heat is taken out from the system at constant temperature
C. At equilibrium
D. In any spontaneous process

Answer

To determine when the entropy of a system decreases, we can analyze the options provided in the question step by step.

### Step 1: Understanding Entropy
Entropy (S) is a measure of the disorder or randomness in a system. The change in entropy (ΔS) can be calculated using the formula:

\[ \Delta S = \frac{Q}{T} \]

where \(Q\) is the heat added to or removed from the system, and \(T\) is the absolute temperature at which the process occurs.

### Step 2: Analyzing the First Option
**Option 1:** When heat is supplied to a system at constant temperature.

- In this case, heat \(Q\) is positive (since heat is being added).
- According to the formula, if \(Q > 0\), then \(\Delta S\) will also be positive.
- Therefore, the entropy of the system increases.

**Conclusion:** This option does not lead to a decrease in entropy.

### Step 3: Analyzing the Second Option
**Option 2:** When heat is taken out from the system at constant temperature.

- Here, heat \(Q\) is negative (since heat is being removed).
- According to the formula, if \(Q < 0\), then \(\Delta S\) will be negative.
- Thus, the entropy of the system decreases.

**Conclusion:** This option leads to a decrease in entropy, making it the correct answer.

### Step 4: Analyzing the Third Option
**Option 3:** In any spontaneous process.

- Spontaneous processes typically lead to an increase in the total entropy of the universe (system + surroundings).
- While the entropy of the system may decrease in some spontaneous processes, the overall entropy of the universe must increase.
- Therefore, this option is not a general case for a decrease in entropy of the system alone.

**Conclusion:** This option does not guarantee a decrease in entropy of the system.

### Final Answer
The correct option where the entropy of a system decreases is **Option 2: When heat is taken out from the system at constant temperature**.

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