The maximum efficiency of a steam engine operating between `100^(@)C and 25^(@)C` is

Options

A. `20%`
B. `22.2%`
C. `25%`
D. `30%`

Answer

To calculate the maximum efficiency of a steam engine operating between two temperatures, we can use the formula derived from the Carnot efficiency. The formula is given by:

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

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

### Step 1: Convert Celsius to Kelvin
First, we need to convert the temperatures from Celsius to Kelvin.

\[ T(K) = T(°C) + 273.15 \]

For \( T_2 = 100°C \):
\[ T_2 = 100 + 273.15 = 373.15 \, K \]

For \( T_1 = 25°C \):
\[ T_1 = 25 + 273.15 = 298.15 \, K \]

### Step 2: Apply the Carnot Efficiency Formula
Now, we can substitute the values of \( T_1 \) and \( T_2 \) into the efficiency formula.

\[ \text{Efficiency} = 1 - \frac{T_1}{T_2} = 1 - \frac{298.15}{373.15} \]

### Step 3: Calculate the Efficiency
Now, we perform the calculation:

1. Calculate \( \frac{298.15}{373.15} \):
\[ \frac{298.15}{373.15} \approx 0.798 \]

2. Now substitute this value back into the efficiency formula:
\[ \text{Efficiency} = 1 - 0.798 \approx 0.202 \]

3. To express this as a percentage, we multiply by 100:
\[ \text{Efficiency} \approx 0.202 \times 100 \approx 20.2\% \]

### Final Answer
The maximum efficiency of the steam engine operating between \( 100°C \) and \( 25°C \) is approximately **20.2%**.

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