During which of the following thermodynamic process represented by PV diagram the heat energy absorbed by system may be equal to area under PV graph?

Options

A.
B.
C.
D. All of these

Answer

To solve the question regarding the thermodynamic process represented by a PV diagram where the heat energy absorbed by the system may be equal to the area under the PV graph, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the PV Diagram**: The area under the PV graph represents the work done (W) during the process. The relationship between heat (Q), internal energy change (ΔU), and work done is given by the first law of thermodynamics:
\[ Q = \Delta U + W \]

2. **Identifying the Conditions for Q = W**: For the heat absorbed (Q) to be equal to the work done (W), the change in internal energy (ΔU) must be zero:
\[ Q = W \quad \text{when} \quad \Delta U = 0 \]
This condition typically occurs in an isothermal process where the temperature remains constant.

3. **Analyzing Different Processes**:
- **Isothermal Process**: In an isothermal process, the temperature is constant, which implies that the internal energy (ΔU) of an ideal gas does not change. Therefore, the heat absorbed (Q) is equal to the work done (W).
- **Adiabatic Process**: In an adiabatic process, there is no heat exchange (Q = 0), so this cannot satisfy our condition.
- **Isobaric Process**: In an isobaric process, the pressure remains constant, which means there is a change in volume and thus a change in internal energy, making Q not equal to W.
- **Isochoric Process**: In an isochoric process, the volume remains constant, meaning no work is done (W = 0), so Q will not equal W.

4. **Identifying the Correct Graph**:
- The isothermal process can be represented by a hyperbolic curve on the PV diagram (P vs. V), where pressure is inversely proportional to volume (P = nRT/V).
- The area under this curve will represent the work done, which equals the heat absorbed.

5. **Conclusion**: The process where the heat energy absorbed by the system is equal to the area under the PV graph is the isothermal process.

### Final Answer:
The correct answer is the **isothermal process** where the heat absorbed (Q) is equal to the work done (W).