Which of the following is a state function?

Options

A. q
B. Work
C. q + w
D. All of these

Answer

To determine which of the given options is a state function, we will analyze each option step by step.

### Step 1: Understand State Functions and Path Functions
- **State Functions**: These are properties that depend only on the state of the system, not on how it got there. Examples include internal energy (U), enthalpy (H), and entropy (S).
- **Path Functions**: These depend on the specific path taken to achieve a particular state. Examples include heat (Q) and work (W).

### Step 2: Analyze Each Option
1. **Option A: Q (Heat)**
- Heat is a path function because the amount of heat transferred depends on the specific process (path) taken. Therefore, Q is not a state function.

2. **Option B: W (Work)**
- Work is also a path function. The work done depends on the path taken during the process. Hence, W is not a state function.

3. **Option C: Q + W**
- According to the first law of thermodynamics, the change in internal energy (ΔU) is given by ΔU = Q + W. The change in internal energy depends only on the initial and final states of the system, making ΔU a state function. Therefore, Q + W represents a state function.

4. **Option D: All of them**
- Since both Q and W are path functions, this option is incorrect.

### Conclusion
The only option that represents a state function is **Option C: Q + W**, which corresponds to the change in internal energy (ΔU).

### Final Answer
The correct answer is **C: Q + W**.

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