According to the third law of thermodynamics which one of the following quantities for a perfectly crystalline solid is zero at absolute zero?
(a)Free energy
(b)Entropy
(c)Enthalpy
(d)Internal energy

Options

A. Free energy
B. Entropy
C. Enthalpy
D. Internal energy

Explanation

To solve the question regarding the third law of thermodynamics and its implications for a perfectly crystalline solid at absolute zero, we will analyze the options provided one by one.

### Step-by-Step Solution:

1. **Understanding the Third Law of Thermodynamics**:
- The third law states that as the temperature of a system approaches absolute zero (0 Kelvin), the entropy of a perfectly crystalline substance approaches zero. This is because, at absolute zero, the system is in its ground state, and there is no disorder or randomness.

2. **Analyzing the Options**:
- **(a) Free energy**: Free energy is a thermodynamic potential that measures the useful work obtainable from a system at constant temperature and pressure. It does not necessarily become zero at absolute zero.
- **(b) Entropy**: As stated earlier, the entropy of a perfectly crystalline solid approaches zero at absolute zero. This aligns with the third law of thermodynamics.
- **(c) Enthalpy**: Enthalpy is a measure of total energy of a thermodynamic system. It does not become zero at absolute zero; it can still have a value depending on the system.
- **(d) Internal energy**: Internal energy is the total energy contained within a system. While it may change with temperature, it does not necessarily become zero at absolute zero.

3. **Conclusion**:
- Based on the analysis, the only quantity that is defined to be zero for a perfectly crystalline solid at absolute zero is **(b) Entropy**.

### Final Answer:
The correct answer is **(b) Entropy**.

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