If a Carnot engine works between `127^@C and 727^@C`, then its efficiency is

Options

A. 0.6
B. 0.4
C. 0.5
D. 0.75

Answer

To find the efficiency of a Carnot engine working between two temperatures, we can use the formula for efficiency (η):

\[ η = 1 - \frac{T_L}{T_H} \]

where:
- \(T_L\) is the absolute temperature of the cold reservoir (sink),
- \(T_H\) is the absolute temperature of the hot reservoir (source).

### Step 1: Convert the temperatures from Celsius to Kelvin
The temperatures given are:
- Hot reservoir temperature \(T_H = 727^\circ C\)
- Cold reservoir temperature \(T_L = 127^\circ C\)

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

Calculating for \(T_H\):
\[ T_H = 727 + 273 = 1000 \, K \]

Calculating for \(T_L\):
\[ T_L = 127 + 273 = 400 \, K \]

### Step 2: Substitute the temperatures into the efficiency formula
Now we can substitute \(T_L\) and \(T_H\) into the efficiency formula:
\[ η = 1 - \frac{T_L}{T_H} = 1 - \frac{400}{1000} \]

### Step 3: Calculate the efficiency
Now, we perform the calculation:
\[ η = 1 - 0.4 = 0.6 \]

### Conclusion
The efficiency of the Carnot engine is:
\[ η = 0.6 \]

### Final Answer
The efficiency of the Carnot engine is 0.6 or 60%.

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