In which of the following cases entropy decreases?

Options

A. Solid changing to liquid
B. Expansion of a gas
C. polymerisation
D. All of these

Answer

To determine in which case entropy decreases, let's analyze the options provided step by step.

### Step 1: Understanding Entropy
Entropy is a measure of the randomness or disorder of a system. A higher entropy indicates a greater degree of disorder, while a lower entropy indicates a more ordered state.

### Step 2: Analyze the First Option - Solid Changing to Liquid
- In this case, a solid is changing to a liquid.
- In solids, particles are closely packed and have limited movement, resulting in lower entropy.
- When a solid melts into a liquid, the particles gain energy, move more freely, and occupy a larger volume.
- Therefore, the randomness increases, and the entropy of the system **increases**.

**Hint:** Remember that solids have lower entropy due to closely packed particles, while liquids have higher entropy due to more freedom of movement.

### Step 3: Analyze the Second Option - Expansion of Gas
- Here, we consider the expansion of a gas.
- When a gas expands, it occupies a larger volume, allowing its particles to move more freely.
- This increase in volume and freedom of movement leads to an increase in randomness.
- Hence, the entropy of the system **increases** during gas expansion.

**Hint:** Think about how gas particles behave in a confined space versus a larger space; more space means more randomness.

### Step 4: Analyze the Third Option - Polymerization
- In polymerization, smaller molecules (monomers) combine to form larger molecules (polymers).
- This process typically results in a decrease in the number of particles in the system.
- When the number of particles decreases, the randomness or disorder of the system also decreases.
- Therefore, the entropy of the system **decreases** during polymerization.

**Hint:** Consider how combining multiple particles into fewer particles affects the overall disorder of the system.

### Conclusion
After analyzing all the options:
- The first option (solid to liquid) results in increased entropy.
- The second option (expansion of gas) also results in increased entropy.
- The third option (polymerization) results in decreased entropy.

Thus, the case in which entropy decreases is **option 3: polymerization**.