If a carnot engine works between `127^(@)C` and `527^(@)C` then its efficiency is

Options

A. 0.25
B. 0.375
C. 0.5
D. 0.75

Answer

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

### Step 1: Convert the temperatures from Celsius to Kelvin
The temperatures given are:
- \( T_1 = 527^\circ C \)
- \( T_2 = 127^\circ C \)

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

Calculating:
\[ T_1 = 527 + 273.15 = 800.15 \approx 800 \, K \]
\[ T_2 = 127 + 273.15 = 400.15 \approx 400 \, K \]

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

Here, \( T_{lower} = T_2 = 400 \, K \) and \( T_{higher} = T_1 = 800 \, K \).

### Step 3: Substitute the values into the efficiency formula
Substituting the values into the formula:
\[ \eta = 1 - \frac{400}{800} \]

### Step 4: Simplify the expression
Calculating the fraction:
\[ \frac{400}{800} = \frac{1}{2} \]

Now substituting back:
\[ \eta = 1 - \frac{1}{2} = \frac{1}{2} \]

### Step 5: Convert the efficiency to a percentage (if needed)
To express the efficiency as a percentage:
\[ \eta = \frac{1}{2} \times 100\% = 50\% \]

### Final Answer
The efficiency of the Carnot engine is \( 0.5 \) or \( 50\% \).

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