Assertion : In adiabatic system, `DeltaU=w_(ad.)`
Reason : In adiabatic system, no transfer of heat takes place.

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 the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding the Assertion:**
- The assertion states that in an adiabatic system, the change in internal energy (ΔU) is equal to the work done (W_ad).
- Recall that an adiabatic process is one where no heat is exchanged with the surroundings (Q = 0).

2. **Applying the First Law of Thermodynamics:**
- According to the first law of thermodynamics, the change in internal energy (ΔU) is given by the equation:
\[ \Delta U = Q + W \]
- In an adiabatic process, since there is no heat transfer (Q = 0), the equation simplifies to:
\[ \Delta U = 0 + W \implies \Delta U = W \]
- This confirms that the assertion is correct.

3. **Understanding the Reason:**
- The reason states that in an adiabatic system, no transfer of heat takes place.
- This is a fundamental characteristic of an adiabatic process, confirming that Q = 0.

4. **Evaluating the Relationship:**
- Since the reason accurately describes the condition of an adiabatic system, it supports the assertion that ΔU = W_ad.
- Therefore, both the assertion and the reason are true, and the reason provides the correct explanation for the assertion.

5. **Conclusion:**
- Both the assertion and the reason are true, and the reason is indeed the correct explanation of the assertion.

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

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