Which of the following proceeds with decrea se in entropy?

Options

A. Boiling of an egg
B. Combustion of benzene at `27^@C`
C. Dissolution of sugar in water
D. Calcination of solid `CaCO_3`

Answer

To determine which of the following processes proceeds with a decrease in entropy, we need to analyze each option based on the concept of entropy, which is a measure of the disorder or randomness of a system.

### Step-by-Step Solution:

1. **Understanding Entropy**:
- Entropy (S) is a measure of the disorder or randomness of particles in a system. Higher entropy indicates greater disorder, while lower entropy indicates more order.

2. **Analyzing Each Option**:
- **Option 1: Boiling of an Egg**:
- When an egg is boiled, the proteins in the egg unfold and change from a more ordered state (raw egg) to a less ordered state (cooked egg).
- This process increases the disorder of the system, leading to an increase in entropy.

- **Option 2: Combustion of Benzene at 27°C**:
- During combustion, energy is released, and the temperature of the system increases.
- Higher temperature corresponds to higher average kinetic energy of particles, which increases their randomness. Thus, the entropy of the system increases.

- **Option 3: Dissolution of Sugar in Water**:
- When sugar dissolves in water, the solid sugar (which is more ordered) becomes dispersed in the liquid (which is less ordered).
- This results in an increase in disorder and therefore an increase in entropy.

- **Option 4: Calcination of Solid Calcium Carbonate**:
- Calcination involves heating calcium carbonate, which breaks it down into calcium oxide and carbon dioxide gas.
- The gaseous state has much higher entropy than the solid state due to greater particle movement and disorder, thus increasing the entropy.

3. **Conclusion**:
- Among the options analyzed, the only process that results in a decrease in entropy is the boiling of an egg. Therefore, the correct answer is:
- **Option 1: Boiling of an Egg**.