A scientist says that the efficiency of his heat engine which operates at source temperature `127^(@)C` and sink temperature `27^(@)C` is `26%`, then

Options

A. it is impossible
B. it is possible with high probability
C. it is possible with low probability
D. data are insufficient

Answer

To solve the problem, we need to determine whether the efficiency of the heat engine claimed by the scientist (26%) is possible given the temperatures of the heat source and sink.

### Step-by-Step Solution:

1. **Convert Temperatures to Kelvin**:
- The source temperature \( T_1 = 127^\circ C = 127 + 273 = 400 \, K \)
- The sink temperature \( T_2 = 27^\circ C = 27 + 273 = 300 \, K \)

2. **Calculate Carnot Efficiency**:
- The Carnot efficiency \( \eta_{carnot} \) is given by the formula:
\[ \eta_{carnot} = 1 - \frac{T_2}{T_1} \]
- Plugging in the values:
\[ \eta_{carnot} = 1 - \frac{300}{400} = 1 - 0.75 = 0.25 \, \text{or} \, 25\% \]

3. **Compare Claimed Efficiency with Carnot Efficiency**:
- The scientist claims that the efficiency of his heat engine is 26%.
- According to the Carnot theorem, no engine can have an efficiency greater than the Carnot efficiency.
- Since 26% (claimed efficiency) is greater than 25% (Carnot efficiency), this situation violates the Carnot theorem.

4. **Conclusion**:
- Since the claimed efficiency of 26% exceeds the maximum possible efficiency (25%) determined by the Carnot efficiency, it is impossible for the heat engine to operate at that efficiency.

### Final Answer:
- Therefore, the correct option is: **It is impossible** (Option 1).