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. Date is insufficient

Answer

To solve the problem regarding the efficiency of a heat engine operating between two temperatures, we follow these steps:

### Step-by-Step Solution:

1. **Identify the temperatures**:
- The source temperature \( T_1 \) is given as \( 127^\circ C \).
- The sink temperature \( T_2 \) is given as \( 27^\circ C \).

2. **Convert temperatures to Kelvin**:
- To convert Celsius to Kelvin, we use the formula:
\[ T(K) = T(°C) + 273 \]
- For the source temperature \( T_1 \):
\[ T_1 = 127 + 273 = 400 \, K \]
- For the sink temperature \( T_2 \):
\[ T_2 = 27 + 273 = 300 \, K \]

3. **Calculate the maximum efficiency**:
- The maximum efficiency \( \eta_{max} \) of a heat engine operating between two temperatures is given by:
\[ \eta_{max} = 1 - \frac{T_2}{T_1} \]
- Substituting the values of \( T_1 \) and \( T_2 \):
\[ \eta_{max} = 1 - \frac{300}{400} \]
- Simplifying this gives:
\[ \eta_{max} = 1 - 0.75 = 0.25 \]

4. **Convert efficiency to percentage**:
- To express the efficiency as a percentage, we multiply by 100:
\[ \eta_{max} \times 100 = 0.25 \times 100 = 25\% \]

5. **Compare with the given efficiency**:
- The scientist claims that the efficiency of the heat engine is \( 26\% \).
- Since the maximum possible efficiency \( 25\% \) is less than the claimed efficiency \( 26\% \), this is impossible.

6. **Conclusion**:
- Therefore, the claim of \( 26\% \) efficiency is incorrect.

### Final Answer:
The maximum efficiency of the heat engine is \( 25\% \), which means the scientist's claim of \( 26\% \) efficiency is impossible.