Statement I: The specific heat of a gas in an adiabatic process is zwero but it is infinite in an isothermal process.
Statement II: Specific heat of a gas is directly proportional to heat exchanged with the system and inversely proportional to change in termperature.

Options

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

Answer

To solve the question, we need to analyze both statements provided and determine their validity.

### Step-by-step Solution:

1. **Understanding Specific Heat**:
- Specific heat (C) is defined as the amount of heat (Q) required to raise the temperature of a unit mass (m) of a substance by one degree Celsius (or one Kelvin). The formula can be expressed as:
\[ C = \frac{Q}{m \Delta T} \]
where \( \Delta T \) is the change in temperature.

2. **Analyzing Statement I**:
- **Adiabatic Process**: In an adiabatic process, there is no heat exchange with the surroundings, which means \( Q = 0 \). Therefore, the specific heat can be calculated as:
\[ C = \frac{Q}{m \Delta T} = \frac{0}{m \Delta T} = 0 \]
- **Isothermal Process**: In an isothermal process, the temperature remains constant, which means \( \Delta T = 0 \). If we substitute this into the specific heat formula, we get:
\[ C = \frac{Q}{m \Delta T} = \frac{Q}{m \cdot 0} \]
This leads to an undefined situation, which we interpret as infinite specific heat since any finite amount of heat can be added without changing the temperature. Thus, the specific heat in an isothermal process is considered infinite.

- **Conclusion for Statement I**: The first statement is true: the specific heat of a gas in an adiabatic process is 0, and it is infinite in an isothermal process.

3. **Analyzing Statement II**:
- The second statement claims that the specific heat of a gas is directly proportional to the heat exchanged with the system and inversely proportional to the change in temperature. This is consistent with the definition of specific heat:
\[ C \propto \frac{Q}{\Delta T} \]
- This means that if more heat is exchanged (Q increases), the specific heat increases, and if the change in temperature (\( \Delta T \)) decreases, the specific heat also increases.

- **Conclusion for Statement II**: The second statement is also true.

4. **Final Conclusion**:
- Both statements are true, and Statement II correctly explains Statement I. Therefore, the correct answer is that both statements are true, and the second statement is the correct explanation of the first statement.

### Final Answer:
Both Statement I and Statement II are true, and Statement II is the correct explanation of Statement I.

---