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 operating between two temperatures, we can use the formula for the efficiency of a Carnot engine, which is given by:

\[ \text{Efficiency} = 1 - \frac{T_2}{T_1} \]

where:
- \( T_1 \) is the absolute temperature of the hot reservoir (in Kelvin),
- \( T_2 \) is the absolute temperature of the cold reservoir (in Kelvin).

### Step 1: Convert the temperatures from Celsius to Kelvin
The temperatures given in the question are:
- Hot reservoir temperature \( T_1 = 727^\circ C \)
- Cold reservoir temperature \( T_2 = 127^\circ C \)

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

Calculating for \( T_1 \):
\[ T_1 = 727 + 273.15 = 1000.15 \, K \approx 1000 \, K \]

Calculating for \( T_2 \):
\[ T_2 = 127 + 273.15 = 400.15 \, K \approx 400 \, K \]

### Step 2: Substitute the values into the efficiency formula
Now that we have the temperatures in Kelvin, we can substitute \( T_1 \) and \( T_2 \) into the efficiency formula:
\[ \text{Efficiency} = 1 - \frac{T_2}{T_1} = 1 - \frac{400}{1000} \]

### Step 3: Perform the calculation
Calculating the fraction:
\[ \frac{400}{1000} = 0.4 \]

Now substituting back into the efficiency formula:
\[ \text{Efficiency} = 1 - 0.4 = 0.6 \]

### Step 4: Convert efficiency to percentage (if needed)
To express the efficiency as a percentage:
\[ \text{Efficiency} = 0.6 \times 100 = 60\% \]

Thus, the efficiency of the Carnot engine is \( 0.6 \) or \( 60\% \).

### Final Answer:
The efficiency of the Carnot engine is \( 0.6 \) or \( 60\% \).

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