What would be the heat absorbed by the system in the cyclic process?

Options

A. `-2PV`
B. zero
C. 2PV
D. PV

Explanation

To solve the question regarding the heat absorbed by the system in a cyclic process, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Cyclic Process**:
In a cyclic process, the system returns to its initial state after completing a cycle. This means that all state functions, including internal energy (U), will have the same value at the beginning and end of the cycle.

**Hint**: Remember that in a cyclic process, the initial and final states are the same.

2. **Change in Internal Energy (ΔU)**:
Since the internal energy of the system is a state function, the change in internal energy (ΔU) over one complete cycle is zero:
\[ \Delta U = 0 \]

**Hint**: State functions depend only on the current state, not on how the system got there.

3. **First Law of Thermodynamics**:
According to the first law of thermodynamics, the relationship between heat (Q), work (W), and internal energy (U) is given by:
\[ \Delta U = Q - W \]
Rearranging this gives:
\[ Q = \Delta U + W \]

**Hint**: The first law of thermodynamics relates heat, work, and internal energy.

4. **Substituting ΔU**:
Since we established that ΔU = 0 for a cyclic process, we can substitute this into the equation:
\[ Q = 0 + W \]
Therefore, we have:
\[ Q = W \]

**Hint**: If ΔU is zero, then all the heat absorbed is converted into work done.

5. **Work Done in a Cyclic Process**:
The work done (W) in a cyclic process can be represented by the area enclosed by the pressure-volume (PV) curve. For a given process, if the area under the curve is represented as pV, then:
\[ W = pV \]

**Hint**: The area under the PV curve represents the work done during the process.

6. **Conclusion**:
Since we have established that the heat absorbed (Q) is equal to the work done (W), we can conclude that:
\[ Q = pV \]
Therefore, the heat absorbed by the system in the cyclic process is \( pV \).

### Final Answer:
The heat absorbed by the system in the cyclic process is \( pV \).