Assertion: In free expansion of a gas inside an aidabatic chamber Q, W and `DeltaU` all are zero.
Reason: In such an expansion `pprop1/V`.

Options

A. (a) If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. (b) If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. (c) If Assertion is true, but the Reason is false.
D. (d) If Assertion is false but the Reason is true.

Explanation

To solve the question, we need to analyze both the assertion and the reason provided:

### Step 1: Understand the Assertion
The assertion states that in the free expansion of a gas inside an adiabatic chamber, the heat transfer (Q), work done (W), and change in internal energy (ΔU) are all zero.

### Step 2: Analyze the Free Expansion Process
In a free expansion process, a gas expands into a vacuum without doing any work on the surroundings. Since there is no external pressure opposing the expansion, the work done (W) is zero.

### Step 3: Apply the First Law of Thermodynamics
The first law of thermodynamics is given by:
\[ \Delta U = Q - W \]
In an adiabatic process, there is no heat exchange with the surroundings, so:
\[ Q = 0 \]
Since we established that \( W = 0 \) in free expansion, we can substitute these values into the first law equation:
\[ \Delta U = 0 - 0 = 0 \]
Thus, the change in internal energy (ΔU) is also zero.

### Step 4: Conclusion for the Assertion
Since Q, W, and ΔU are all zero, the assertion is true.

### Step 5: Understand the Reason
The reason states that in such an expansion, pressure (p) is directly proportional to \( \frac{1}{V} \).

### Step 6: Analyze the Reason
In an ideal gas, the relationship given by the ideal gas law is:
\[ PV = nRT \]
If the temperature (T) is constant (which we will show later), then:
\[ P \propto \frac{1}{V} \]
This means that as volume increases, pressure decreases, confirming the relationship stated in the reason.

### Step 7: Conclusion for the Reason
Since the pressure is indeed inversely proportional to volume in a constant temperature scenario, the reason is also true.

### Final Conclusion
Both the assertion and reason are true, and the reason correctly explains the assertion.

### Final Answer
Both the assertion and reason are true, and the reason is the correct explanation for the assertion.

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