Assertion : Efficiency of a Carnot engine increase on reducing the temperature of sink. Reason : The efficiency of a Carnot engine is defined as ratio of net mechanical work done per cycle by the gas to the amount of heat energy absorbed per cycle from the source.

Options

A. Statement-1 is true, statement-2 is true, statement-2 is a correct explanation for statement-1
B. Statement-1 is true, statement-2 is true, statement-2 is NOT a correct explanation for statement-1
C. Statement-1 is true, statement-2 is false
D. Statement-1 is false, statement-2 is true

Answer

To solve the question, we need to analyze the assertion and reason provided regarding the efficiency of a Carnot engine.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that the efficiency of a Carnot engine increases when the temperature of the sink (T2) is reduced.
- The efficiency of a Carnot engine is given by the formula:
\[ \eta = 1 - \frac{T_2}{T_1} \]
- Here, \(T_1\) is the temperature of the heat source and \(T_2\) is the temperature of the heat sink.

2. **Analyzing the Efficiency Formula**:
- From the efficiency formula, we can see that if we decrease \(T_2\) (the temperature of the sink), the term \(\frac{T_2}{T_1}\) becomes smaller.
- As a result, the efficiency \(\eta\) increases because the overall value of \(1 - \frac{T_2}{T_1}\) becomes larger.

3. **Understanding the Reason**:
- The reason states that the efficiency of a Carnot engine is defined as the ratio of net mechanical work done per cycle (W) to the amount of heat energy absorbed per cycle from the source (Q1).
- This definition is correct:
\[ \eta = \frac{W}{Q_1} \]
- However, it does not directly explain why reducing the temperature of the sink increases efficiency.

4. **Conclusion**:
- Both the assertion and the reason are correct statements.
- However, the reason provided does not serve as a correct explanation for the assertion because it does not address the relationship between sink temperature and efficiency directly.

### Final Answer:
- The assertion is true, the reason is true, but the reason is not a correct explanation for the assertion.