A system works in a cyclic process. It absorbs `20` calories of heat and rejects `60 J` of heat during the process. The magnitude of work done `(J)` is `[ 1 "calorie"=4.2 J]`:

Answer

To solve the problem step by step, we will use the principles of thermodynamics, particularly focusing on the first law, which states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (Q) minus the work done by the system (W).

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Heat absorbed by the system (Q1) = 20 calories
- Heat rejected by the system (Q2) = 60 J
- Conversion factor: 1 calorie = 4.2 J

2. **Convert Heat Absorbed to Joules**:
- Convert Q1 from calories to joules:
\[ Q1 = 20 \text{ calories} \times 4.2 \text{ J/calorie} = 84 \text{ J} \]

3. **Apply the First Law of Thermodynamics**:
- For a cyclic process, the change in internal energy (ΔU) is zero:
\[ \Delta U = Q - W = 0 \]
- Rearranging gives:
\[ W = Q - \Delta U \]
- Since ΔU = 0, we have:
\[ W = Q \]

4. **Calculate the Total Heat (Q)**:
- The total heat (Q) absorbed by the system is the heat absorbed minus the heat rejected:
\[ Q = Q1 - Q2 \]
- Substitute the values:
\[ Q = 84 \text{ J} - 60 \text{ J} = 24 \text{ J} \]

5. **Determine the Work Done (W)**:
- Since W is equal to the net heat absorbed, we have:
\[ W = 24 \text{ J} \]

6. **Find the Magnitude of Work Done**:
- The magnitude of work done is simply the absolute value:
\[ |W| = 24 \text{ J} \]

### Final Answer:
The magnitude of work done is **24 J**.