Which of the following is a state function?

Options

A. q + w
B. Entropy
C. Free Energy
D. All of these

Answer

To determine which of the given options is a state function, we will analyze each option based on the definitions of state functions and path functions in thermodynamics.

### Step-by-Step Solution:

1. **Understand the Definitions**:
- **State Function**: A property whose value depends only on the state of the system (initial and final states) and not on the path taken to reach that state. Examples include internal energy, enthalpy, entropy, and Gibbs free energy.
- **Path Function**: A property whose value depends on the specific path taken to reach the final state. Examples include heat (Q) and work (W).

2. **Evaluate Each Option**:
- **Option A: Q + W**:
- Both Q (heat) and W (work) are path functions. However, according to the first law of thermodynamics, the change in internal energy (ΔU) is given by ΔU = Q + W. Internal energy is a state function. Therefore, Q + W represents a change in a state function (internal energy), making it a state function as well.

- **Option B: Entropy**:
- Entropy is a well-known state function. It depends only on the initial and final states of the system, not on how the change occurs.

- **Option C: Free Energy**:
- Free energy (Gibbs free energy) is also a state function. Like entropy, it depends only on the state of the system and not on the path taken to reach that state.

- **Option D: All of these**:
- Since Q + W is a state function, entropy is a state function, and free energy is a state function, this option is correct.

3. **Conclusion**:
- All the options provided (Q + W, entropy, and free energy) are state functions. Therefore, the correct answer is **Option D: All of these**.

### Final Answer:
**Option D: All of these**