Statement-1: The internal energy of a system does not change when there is not change in temperature
Statement-2: The internal energy of a gaseous system is state function.

Options

A. Statement-1 is true, statement-2 is true, statement-2 is a correct explanation for statement-1
B. Statement-1 is true, statement-2 is true, statement-2 is NOT a correct explanation for statement-1
C. Statement-1 is true, statement-2 is false
D. Statement-1 is false, statement-2 is true

Answer

To analyze the two statements provided in the question, we will evaluate each statement based on the principles of thermodynamics.

### Step-by-Step Solution:

**Step 1: Evaluate Statement 1**
- **Statement 1**: "The internal energy of a system does not change when there is no change in temperature."
- Internal energy (U) is a function of state, which means it depends on the state variables of the system, such as temperature (T) and volume (V).
- For an ideal gas, the internal energy is primarily a function of temperature. However, for real gases and fluids, internal energy can also depend on volume.
- If the temperature remains constant (dT = 0), but the volume changes (dV ≠ 0), the internal energy can still change. Therefore, this statement is not universally true.

**Conclusion for Statement 1**: This statement is **false** because internal energy can change even if the temperature does not, especially in non-ideal systems.

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**Step 2: Evaluate Statement 2**
- **Statement 2**: "The internal energy of a gaseous system is a state function."
- A state function is a property that depends only on the current state of the system, not on the path taken to reach that state.
- The internal energy of a gaseous system is indeed a state function, as it depends on state variables like temperature and volume. It does not depend on how the system reached its current state.
- Therefore, this statement is true.

**Conclusion for Statement 2**: This statement is **true** because internal energy is a state function for gaseous systems.

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### Final Conclusion:
- **Statement 1**: False
- **Statement 2**: True

The correct answer is that Statement 1 is false and Statement 2 is true.