Assertion: The value of specific heat of a gas at constant pressure is greater than its value at constant volume.
Reason: Some heat is consumed for the expansion of the gas.

Options

A. A if both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. If both Assertion and Reason are true but Reason is not correct explanation of the Assertion.
C. If Assertion is true but the Reason is false.
D. lf Assertion is false but Reason is true.

Answer

To solve the question, we need to analyze the assertion and reason provided:

**Assertion:** The value of specific heat of a gas at constant pressure (Cp) is greater than its value at constant volume (Cv).

**Reason:** Some heat is consumed for the expansion of the gas.

### Step-by-Step Solution:

1. **Understanding Specific Heat Capacities:**
- Specific heat at constant pressure (Cp) is the amount of heat required to raise the temperature of a unit mass of gas by one degree Celsius while maintaining constant pressure.
- Specific heat at constant volume (Cv) is the amount of heat required to raise the temperature of a unit mass of gas by one degree Celsius while maintaining constant volume.

2. **Analyzing the Assertion:**
- It is a well-established fact in thermodynamics that Cp is always greater than Cv for an ideal gas. This is because when heat is added at constant pressure, some of that heat is used to do work on the surroundings as the gas expands.

3. **Understanding the Reason:**
- The reason states that some heat is consumed for the expansion of the gas. This is true because when a gas expands at constant pressure, it does work against the external pressure, which requires energy. This energy comes from the heat supplied to the system.

4. **Connecting Assertion and Reason:**
- Since some of the heat added at constant pressure is used for expansion, the remaining heat goes into increasing the internal energy (and thus the temperature) of the gas. Therefore, more heat is required to achieve the same temperature change at constant pressure compared to constant volume.

5. **Conclusion:**
- Both the assertion and the reason are true, and the reason correctly explains why the assertion is true. Therefore, the correct answer to the question is that both the assertion and reason are true, and the reason explains the assertion.

### Final Answer:
Both the assertion and reason are true, and the reason explains the assertion.

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