Assertion: Under adiabatic free expansion, `((dU)/(dV))_(T)` is +ve when attractive forces are dominant between gas molecules [U,V,T respresent internal energy, volume and temperature of gas respectively]
Reason: Internal energy is a state function.

Options

A. Statement-I is true, statement-II is true and statement-II is correct explanation for statement-I
B. Statement-I is true, statement-II is true and statement-II is NOT correct explanation for statement-I
C. Statement-I is true, statement-II is false
D. Statement-I is false, statement-II is true

Answer

To solve the given question, we need to analyze both the assertion and the reason statements provided.

### Step 1: Analyze the Assertion
The assertion states: "Under adiabatic free expansion, \((\frac{dU}{dV})_{T}\) is positive when attractive forces are dominant between gas molecules."

- In an adiabatic free expansion, a gas expands into a vacuum without performing work and without heat exchange.
- When attractive forces between gas molecules are dominant, as the volume increases, the molecules tend to move apart against these attractive forces.
- This movement requires energy, which comes from the internal energy of the gas.
- Therefore, as the volume increases, the internal energy \(U\) must increase to compensate for the energy required to overcome the attractive forces.
- Hence, \((\frac{dU}{dV})_{T}\) becomes positive.

**Conclusion for Assertion**: The assertion is true.

### Step 2: Analyze the Reason
The reason states: "Internal energy is a state function."

- A state function is a property that depends only on the state of the system and not on how that state was reached.
- Internal energy \(U\) is indeed a state function because it depends only on the current state (temperature, pressure, volume) of the system and not on the path taken to reach that state.
- Therefore, this statement is also true.

**Conclusion for Reason**: The reason is true.

### Step 3: Determine the Relationship
Now, we need to determine if the reason is the correct explanation of the assertion.

- The assertion discusses the behavior of internal energy during adiabatic free expansion due to attractive forces, while the reason simply states that internal energy is a state function.
- The reason does not explain why the assertion is true; it merely states a fact about internal energy.

### Final Conclusion
Both the assertion and the reason are true, but the reason is not the correct explanation for the assertion. Therefore, the correct answer is that the assertion is true, the reason is true, but the reason is not the correct explanation of the assertion.

### Answer: Option B
- Statement one is true.
- Statement two is true.
- Statement two is not the correct explanation of statement one.

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