Find the efficiency of carnot engine whose source and sink are at `927^(@)C` and `27^(@)C`.

Explanation

To find the efficiency of a Carnot engine operating between two temperatures, we can follow these steps:

### Step 1: Convert the temperatures from Celsius to Kelvin
The temperatures provided are:
- Source temperature (TH) = 927°C
- Sink temperature (TL) = 27°C

To convert Celsius to Kelvin, we use the formula:
\[ T(K) = T(°C) + 273.15 \]

Calculating the temperatures:
- \( TH = 927 + 273.15 = 1200.15 \, K \) (approximately 1200 K)
- \( TL = 27 + 273.15 = 300.15 \, K \) (approximately 300 K)

### Step 2: Use the formula for the efficiency of a Carnot engine
The efficiency (η) of a Carnot engine is given by the formula:
\[ \eta = 1 - \frac{TL}{TH} \]

### Step 3: Substitute the values into the efficiency formula
Substituting the values we calculated:
\[ \eta = 1 - \frac{300}{1200} \]

### Step 4: Simplify the expression
Calculating the fraction:
\[ \frac{300}{1200} = \frac{1}{4} \]

Now substituting back:
\[ \eta = 1 - \frac{1}{4} = 1 - 0.25 = 0.75 \]

### Step 5: Convert the efficiency to percentage
To express the efficiency as a percentage, we multiply by 100:
\[ \eta = 0.75 \times 100 = 75\% \]

### Final Answer
The efficiency of the Carnot engine is **75%**.

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