In which of the following process work behaves as state function :

Options

A. Isothermal
B. Isochoric
C. Adiabatic
D. Isobaric

Explanation

To determine in which of the following processes work behaves as a state function, we need to analyze the characteristics of different thermodynamic processes.

### Step-by-Step Solution:

1. **Understanding State Functions**:
- State functions are properties that depend only on the state of the system, not on the path taken to reach that state. Examples include internal energy (U), enthalpy (H), and entropy (S). Work (W) and heat (q) are not state functions because they depend on the process.

2. **Analyzing Different Processes**:
- **Adiabatic Process**: In an adiabatic process, there is no heat exchange (q = 0). According to the first law of thermodynamics:
\[ \Delta U = q + W \]
Since q = 0, we have:
\[ \Delta U = W \]
This means the work done is equal to the change in internal energy, which is a state function. Hence, in an adiabatic process, work can be related to a state function.

- **Isothermal Process**: In an isothermal process, the temperature remains constant, and heat is exchanged with the surroundings. Here, work done is not solely dependent on the state of the system, as it involves heat transfer.

- **Isochoric Process**: In an isochoric process, the volume remains constant, and no work is done (W = 0). However, this does not imply that work behaves as a state function.

- **Isobaric Process**: In an isobaric process, the pressure remains constant, and work is done by the system as it expands or contracts. Again, work is not a state function here.

3. **Conclusion**:
- The only process among the options where work can be directly related to a state function (change in internal energy) is the **adiabatic process**.

Thus, the correct answer is that work behaves as a state function in the **adiabatic process**.