If a carnot engine works as temperature between 300 to 400 K. then find the efficiency of that engine

Answer

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

### Step-by-Step Solution:

1. **Identify the Temperatures**:
- The temperatures given in the problem are:
- \( T_1 = 400 \, K \) (Hot reservoir)
- \( T_2 = 300 \, K \) (Cold reservoir)

2. **Use the Efficiency Formula for a Carnot Engine**:
- The efficiency \( \eta \) of a Carnot engine is given by the formula:
\[ \eta = 1 - \frac{T_2}{T_1} \]

3. **Substitute the Values into the Formula**:
- Plugging in the values of \( T_1 \) and \( T_2 \):
\[ \eta = 1 - \frac{300}{400} \]

4. **Calculate the Fraction**:
- Simplifying the fraction:
\[ \frac{300}{400} = \frac{3}{4} = 0.75 \]

5. **Complete the Calculation**:
- Now, substitute back into the efficiency formula:
\[ \eta = 1 - 0.75 = 0.25 \]

6. **Convert to Percentage (if needed)**:
- To express the efficiency as a percentage, multiply by 100:
\[ \eta = 0.25 \times 100 = 25\% \]

### Final Answer:
The efficiency of the Carnot engine is \( 0.25 \) or \( 25\% \).

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