A : Heat absorbed in a cyclic process is zero.
R : Work done in a cyclic process is zero.

Options

A. If both Assertion & Reason are true and the reason is the correct explantion of the assertion, then mark(1)
B. If both Assertion & Reason are true but the reason is not the correct explanation of the assertion, then mark (2).
C. If Assertion is true statement but Reason is false, then mark (3).
D. If both Assertion and Reason are false statements, then mark (4)

Answer

To solve the problem, we need to analyze the assertion (A) and the reason (R) given in the question:

**Assertion (A):** Heat absorbed in a cyclic process is zero.
**Reason (R):** Work done in a cyclic process is zero.

### Step-by-step Solution:

1. **Understanding the Assertion:**
- In a cyclic process, a system returns to its initial state after completing a cycle. According to the first law of thermodynamics, the change in internal energy (ΔU) over a complete cycle is zero because the initial and final states are the same.
- The first law of thermodynamics states: ΔU = Q - W, where Q is the heat absorbed and W is the work done by the system.
- Since ΔU = 0 for a complete cycle, we have Q = W. This means that the heat absorbed is equal to the work done, not necessarily zero.

2. **Understanding the Reason:**
- The reason states that the work done in a cyclic process is zero. To analyze this, we can refer to the P-V diagram of a cyclic process.
- In a P-V diagram, the work done by the system during a cyclic process is represented by the area enclosed by the cycle. Since there is typically an area enclosed in a cyclic process (unless it is a degenerate case), the work done cannot be zero.

3. **Conclusion on Assertion and Reason:**
- Since the assertion (A) claims that heat absorbed is zero, which is incorrect because heat absorbed equals work done, we conclude that A is false.
- The reason (R) also claims that work done is zero, which is incorrect as we have established that work done in a cyclic process is not zero. Thus, R is also false.

4. **Final Evaluation:**
- Both the assertion and the reason are false. According to the options provided, if both A and R are false, we would select option 4 as the answer.

### Final Answer:
The correct option is 4, as both the assertion and the reason are false.

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