Assertion (A): Internal energy change in a cyclic process is zero.
Reason (R ) : Internal energy is a state funciton.

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 regarding the assertion and reason provided, we can break it down into a step-by-step analysis:

### Step 1: Understand the Assertion
The assertion states that the internal energy change in a cyclic process is zero. A cyclic process is one where the system returns to its initial state after completing a series of changes.

### Step 2: Analyze the Cyclic Process
In a cyclic process, the system undergoes various transformations but ultimately returns to its starting point. Since internal energy is a state function, the change in internal energy (ΔU) depends only on the initial and final states of the system.

### Step 3: Apply the Concept of State Functions
Since the internal energy is a state function, it does not depend on the path taken to reach the final state. Therefore, if the system returns to its original state, the change in internal energy must be zero (ΔU = U_final - U_initial = 0 when U_final = U_initial).

### Step 4: Conclusion on the Assertion
Thus, the assertion that the internal energy change in a cyclic process is zero is correct.

### Step 5: Understand the Reason
The reason states that internal energy is a state function. This means that the value of internal energy is determined solely by the state of the system (characterized by properties such as temperature, pressure, and volume) and not by how the system reached that state.

### Step 6: Link the Reason to the Assertion
Since the assertion is correct and the reason explains why the assertion is true (because internal energy being a state function implies that the change in internal energy is zero when returning to the same state), the reason also holds true.

### Final Conclusion
Both the assertion and the reason are correct, and the reason provides a valid explanation for the assertion.

### Summary of the Solution
1. The assertion is that the internal energy change in a cyclic process is zero.
2. The reason is that internal energy is a state function.
3. Both statements are correct, and the reason explains the assertion.