A carnot engine works between temperatures `327^(@)C` and `27^(@)C`. If the engine takes 1600 J of heat from the higher temperature reservoir, the work done by the engine per cycle (in Joule) is equal to __________.

Explanation

To solve the problem of calculating the work done by a Carnot engine operating between two temperatures, we can follow these steps:

### Step-by-Step Solution:

1. **Convert Temperatures to Kelvin**:
- The temperatures given are in Celsius. We need to convert them to Kelvin using the formula:
\[ T(K) = T(°C) + 273.15 \]
- For the higher temperature \( T_1 = 327°C \):
\[ T_1 = 327 + 273.15 = 600.15 \approx 600 \, K \]
- For the lower temperature \( T_2 = 27°C \):
\[ T_2 = 27 + 273.15 = 300.15 \approx 300 \, K \]

2. **Calculate the Efficiency of the Carnot Engine**:
- The efficiency \( \eta \) of a Carnot engine is given by:
\[ \eta = 1 - \frac{T_2}{T_1} \]
- Substituting the values:
\[ \eta = 1 - \frac{300}{600} = 1 - 0.5 = 0.5 \]

3. **Calculate the Work Done by the Engine**:
- The work done \( W \) can be calculated using the formula:
\[ W = \eta \times Q_1 \]
- Where \( Q_1 \) is the heat absorbed from the higher temperature reservoir, which is given as 1600 J.
- Substituting the values:
\[ W = 0.5 \times 1600 = 800 \, J \]

### Final Answer:
The work done by the engine per cycle is **800 Joules**.