A certain engine which operates in a Carnot cycle absorbe `3.0 kJ` at `400^(@)C` in a cycle. If it rejects heat at `100^(@)C`, how much work is done on the engine per cycle and how much heat is evolved at `100^(@)C` in each cycle?

Explanation

To solve the problem, we need to find the work done on the engine per cycle and the amount of heat evolved at 100°C in each cycle. We will use the principles of the Carnot cycle and the efficiency of the engine.

### Step-by-Step Solution:

1. **Identify the given data:**
- Heat absorbed (Q2) = 3.0 kJ
- Temperature of the hot reservoir (T2) = 400°C = 400 + 273.15 = 673.15 K
- Temperature of the cold reservoir (T1) = 100°C = 100 + 273.15 = 373.15 K
...