A carnot engine is working in such a temperature of sink that its efficiency is maximum and never changes with any non-zero temperature of source. The temperature of sink will most likely to be

Options

A. 0 K
B. `0^(@)C`
C. `0^(@)F`
D. Data insufficient

Answer

To solve the problem, we need to understand the relationship between the efficiency of a Carnot engine and the temperatures of the heat source and sink.

### Step-by-Step Solution:

1. **Understanding Efficiency of Carnot Engine**:
The efficiency (η) of a Carnot engine is given by the formula:
\[ \eta = 1 - \frac{T_L}{T_H} \]
where:
- \(T_L\) = temperature of the sink (in Kelvin)
- \(T_H\) = temperature of the source (in Kelvin)

2. **Condition of Maximum Efficiency**:
The problem states that the efficiency is maximum and does not change with any non-zero temperature of the source. This implies that the efficiency remains constant regardless of the value of \(T_H\).

3. **Analyzing the Efficiency Formula**:
For the efficiency to remain constant as \(T_H\) changes, the term \(\frac{T_L}{T_H}\) must also remain constant. This can only happen if \(T_L\) is zero, because if \(T_L\) is zero, then:
\[ \eta = 1 - \frac{0}{T_H} = 1 \]
This indicates maximum efficiency.

4. **Conclusion on Sink Temperature**:
Since \(T_L\) must be zero for the efficiency to remain constant and equal to 1, the temperature of the sink must be:
\[ T_L = 0 \text{ Kelvin} \]

5. **Final Answer**:
Therefore, the temperature of the sink will most likely be **0 Kelvin**.