A : The specific heat of an ideal gas is zero in an adiabatic process.
R : Specific heat of a gas is process independent.

Options

A. If both Assertion & Reason are true and the reason is the correct explantion of the assertion, then mark(1)
B. If both Assertion & Reason are true but 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 and Reason are false statements, then mark (4)

Answer

To solve the question, we need to analyze the assertion (A) and the reason (R) provided:

**Assertion (A):** The specific heat of an ideal gas is zero in an adiabatic process.
**Reason (R):** Specific heat of a gas is process independent.

### Step 1: Understand the concept of specific heat
Specific heat (C) is defined as the amount of heat (q) required to change the temperature (ΔT) of a unit mass (m) of a substance. The formula is given by:
\[ q = mc\Delta T \]
From this, we can derive:
\[ C = \frac{q}{m\Delta T} \]

### Step 2: Analyze the adiabatic process
In an adiabatic process, there is no heat exchange with the surroundings, which means:
\[ q = 0 \]
If we substitute this into the specific heat formula, we get:
\[ C = \frac{0}{m\Delta T} = 0 \]
Thus, the specific heat of an ideal gas in an adiabatic process is indeed zero.

### Step 3: Evaluate the reason (R)
The reason states that the specific heat of a gas is process independent. This is incorrect because specific heat can vary depending on the process being conducted (e.g., adiabatic, isothermal, etc.). For example:
- In an isothermal process, the temperature does not change, leading to a different behavior of specific heat.
- In an adiabatic process, since there is no heat exchange, the specific heat is zero.

### Step 4: Conclusion
- The assertion (A) is **true**: The specific heat of an ideal gas is zero in an adiabatic process.
- The reason (R) is **false**: Specific heat is process dependent.

Thus, the correct answer is that assertion A is true and reason R is false.

### Final Answer:
Assertion (A) is true, and Reason (R) is false.

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