Assetion : Specific heat of a gas at constant pressure is greater than its specific heat at constant volume.
This is because at constant pressure, some heat is spent in expansion of the gas.

Options

A. If both assertion and reason are true and reason is the correct explanation os assertion.
B. If both assertion and reason are true but reason is not be correct explanation of assertion.
C. If assertion is true but reason is false.
D. If both assertion and reason are false.

Explanation

To solve the question regarding the assertion and reason about the specific heats of a gas, we can break it down step by step.

### Step-by-Step Solution:

1. **Understanding Specific Heat Capacities**:
- Specific heat at constant volume (\(C_V\)) is defined as the amount of heat required to raise the temperature of a unit mass of gas by one degree Celsius while keeping the volume constant.
- Specific heat at constant pressure (\(C_P\)) is defined as the amount of heat required to raise the temperature of a unit mass of gas by one degree Celsius while keeping the pressure constant.

2. **Mathematical Representation**:
- For a gas, the relationship can be expressed as:
\[ C_V = \left( \frac{dU}{dT} \right)_V \]
\[ C_P = \left( \frac{dH}{dT} \right)_P \]
- Here, \(U\) is the internal energy and \(H\) is the enthalpy of the gas.

3. **Enthalpy and Internal Energy**:
- Enthalpy (\(H\)) is related to internal energy (\(U\)) by the equation:
\[ H = U + PV \]
- At constant pressure, when a gas is heated, it not only increases in internal energy but also does work against the external pressure as it expands.

4. **Heat Transfer at Constant Pressure**:
- When heat is added to a gas at constant pressure, part of that heat goes into increasing the internal energy (\(U\)) and part goes into doing work against the external pressure (expansion work).
- Therefore, the heat added at constant pressure is greater than the heat added at constant volume because of the additional work done during expansion.

5. **Conclusion**:
- Since \(C_P\) accounts for both the increase in internal energy and the work done during expansion, it is always greater than \(C_V\):
\[ C_P > C_V \]
- Thus, the assertion is correct: the specific heat of a gas at constant pressure is greater than its specific heat at constant volume. The reason provided is also correct as it explains why this is the case.

### Final Answer:
Both the assertion and the reason are correct, and the reason is a correct explanation of the assertion.

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