The efficiency of a Carnot engine working between 800 K and 500 K is -

Options

A. 0.45
B. 0.625
C. 0.375
D. 0.5

Answer

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

\[ \eta = 1 - \frac{T_c}{T_h} \]

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

### Step-by-step Solution:

1. **Identify the temperatures**:
- The temperature of the cold reservoir \(T_c = 500 \, K\)
- The temperature of the hot reservoir \(T_h = 800 \, K\)

2. **Substitute the values into the efficiency formula**:
\[ \eta = 1 - \frac{T_c}{T_h} = 1 - \frac{500}{800} \]

3. **Simplify the fraction**:
\[ \frac{500}{800} = \frac{5}{8} \]

4. **Calculate the efficiency**:
\[ \eta = 1 - \frac{5}{8} = \frac{3}{8} \]

5. **Convert the fraction to decimal**:
\[ \frac{3}{8} = 0.375 \]

6. **Final result**:
The efficiency of the Carnot engine is \(0.375\) or \(37.5\%\).