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. Statement I: is true, Statement II is true and Statement II is the correct explanation for Statement I.
B. Statement I: is true, Statement II is true and Statement II is NOT the correct explanation for Statement I.
C. Statement I is true, Statement II is false.
D. Statement I is false, Statement II is true.

Explanation

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

### Step 1: Analyze Statement I
Statement I claims that the specific heat of a gas in an adiabatic process is zero, while in an isothermal process, it is infinite.

- **Adiabatic Process**: In an adiabatic process, there is no heat exchange with the surroundings (dq = 0). The specific heat (C) is defined as:
\[ C = \frac{dq}{dT} \]
Since dq = 0, it follows that:
\[ C = \frac{0}{dT} = 0 \]
Therefore, the specific heat in an adiabatic process is indeed zero.

- **Isothermal Process**: In an isothermal process, the temperature remains constant (dT = 0). The specific heat is again defined as:
\[ C = \frac{dq}{dT} \]
Since dT = 0, it follows that:
\[ C = \frac{dq}{0} = \infty \]
Therefore, the specific heat in an isothermal process is infinite.

**Conclusion for Statement I**: True.

### Step 2: Analyze Statement II
Statement II states 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.

- The specific heat (C) is defined as:
\[ C = \frac{dq}{dT} \]
This means that specific heat is the amount of heat (dq) required to raise the temperature (dT) of a unit mass of the substance by one degree.

- The statement claims that specific heat is directly proportional to dq and inversely proportional to dT. This is misleading because while it is true that:
\[ C \propto dq \quad \text{and} \quad C \propto \frac{1}{dT} \]
it does not imply a direct relationship in the form of a simple proportionality constant. The specific heat is defined through the ratio of these two quantities, not as a direct proportionality.

**Conclusion for Statement II**: False.

### Final Conclusion
- Statement I is true.
- Statement II is false.