A Carnot engine takes 9000 cal of heat from a reservoir at `627^@`C and gives it to a sink at `27^@C`. The work done by the angine is

Options

A. 6 kcal
B. 3 kcal
C. 4 kcal
D. 8 kcal

Answer

To solve the problem of finding the work done by a Carnot engine that takes 9000 calories of heat from a reservoir at 627°C and gives it to a sink at 27°C, we can follow these steps:

### Step 1: Convert temperatures from Celsius to Kelvin
To use the Carnot efficiency formula, we need to convert the temperatures from Celsius to Kelvin.
- The temperature of the hot reservoir (TH) is:
\[ TH = 627 + 273 = 900 \, K \]
- The temperature of the cold sink (TL) is:
\[ TL = 27 + 273 = 300 \, K \]

### Step 2: Calculate the efficiency of the Carnot engine
The efficiency (η) of a Carnot engine is given by the formula:
\[ η = 1 - \frac{TL}{TH} \]
Substituting the values we found:
\[ η = 1 - \frac{300}{900} = 1 - \frac{1}{3} = \frac{2}{3} \]

### Step 3: Calculate the work done by the engine
The work done (W) by the engine can be calculated using the efficiency and the heat absorbed from the hot reservoir (QH):
\[ W = η \times QH \]
Given that \(QH = 9000 \, \text{cal}\):
\[ W = \frac{2}{3} \times 9000 \, \text{cal} = 6000 \, \text{cal} \]

### Step 4: Final answer
The work done by the engine is:
\[ \boxed{6000 \, \text{cal}} \]