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 but less probable
C. It is quite probable
D. Data are incomplete

Explanation

To determine whether the scientist's claim about the efficiency of his heat engine is possible, we will follow these steps:

### Step 1: Convert the temperatures from Celsius to Kelvin
The temperatures given are:
- Source temperature, \( T_1 = 127^\circ C \)
- Sink temperature, \( T_2 = 27^\circ C \)

To convert these temperatures to Kelvin, we use the formula:
\[ T(K) = T(°C) + 273 \]

Calculating the temperatures:
\[ T_1 = 127 + 273 = 400 \, K \]
\[ T_2 = 27 + 273 = 300 \, K \]

### Step 2: Use the formula for efficiency
The efficiency of a heat engine is given by the formula:
\[ \eta = 1 - \frac{T_2}{T_1} \]

Substituting the values we calculated:
\[ \eta = 1 - \frac{300}{400} \]

### Step 3: Simplify the efficiency calculation
Now we simplify the fraction:
\[ \eta = 1 - 0.75 = 0.25 \]

### Step 4: Convert efficiency to percentage
To express the efficiency as a percentage, we multiply by 100:
\[ \eta = 0.25 \times 100 = 25\% \]

### Step 5: Compare with the scientist's claim
The scientist claims that the efficiency of his heat engine is 26%. However, we calculated the maximum possible efficiency based on the temperatures provided to be 25%.

### Conclusion
Since the calculated efficiency (25%) is less than the claimed efficiency (26%), it is impossible for the scientist's claim to be true.

### Final Answer
The scientist's claim that the efficiency of his heat engine is 26% is **not possible**.

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