A: Specific heat is an intensive property
R: Heat capacity is an extensive property.

Options

A. If both Assertion & Reason are true and the reason is the correct explanation of the assertion , then mark (1)
B. If both Assertion & Reason are true and the reason is not the correct explanation of the assertion, then mark (2)
C. If Assertion is true statement but Reason is false, then mark (3)
D. If both Assertion is true statement but Reason is false, then mark (3)

Answer

To solve the question regarding the assertion and reason provided, we will analyze both statements step by step.

### Step 1: Understanding Specific Heat
- **Assertion (A)**: Specific heat is an intensive property.
- **Definition**: Specific heat (often denoted as \(c\)) is defined as the amount of heat required to raise the temperature of one unit mass of a substance by one degree Celsius (or one Kelvin).
- **Intensive Property**: An intensive property is one that does not depend on the amount of substance present. It is a characteristic of the material itself.

**Conclusion for Step 1**: Since specific heat is defined per unit mass and does not change with the quantity of the substance, it is indeed an intensive property.

### Step 2: Understanding Heat Capacity
- **Reason (R)**: Heat capacity is an extensive property.
- **Definition**: Heat capacity (denoted as \(C\)) is the total amount of heat required to change the temperature of a given quantity of a substance by one degree Celsius (or one Kelvin).
- **Extensive Property**: An extensive property is one that depends on the amount of substance present. It changes when the size or extent of the system changes.

**Conclusion for Step 2**: Since heat capacity is related to the total mass of the substance, it is an extensive property.

### Step 3: Analyzing the Relationship Between Assertion and Reason
- Both statements are correct:
- Specific heat is indeed an intensive property.
- Heat capacity is indeed an extensive property.
- However, the reason provided does not explain the assertion. The fact that heat capacity is extensive does not provide a rationale for why specific heat is intensive.

### Final Conclusion
- **Assertion (A)**: True
- **Reason (R)**: True
- **Relationship**: The reason is not the correct explanation for the assertion.

### Answer:
Both the assertion and the reason are correct, but the reason does not explain the assertion. Therefore, the answer is **(b)**.

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