Which of the following are path functions
(A) `W`
(B) `Q`
(C) `Q+W`
(D) `H-TS`

Options

A. A and D
B. A and B
C. A,B and D
D. A,C and D

Answer

To determine which of the given options are path functions, we need to understand the definitions of path functions and state functions in thermodynamics.

### Step 1: Define Path Functions and State Functions
- **Path Functions**: These are properties that depend on the path taken during a process. The value of a path function changes if the path of the process changes.
- **State Functions**: These are properties that depend only on the state of the system and not on how the system reached that state. Their values are determined by the current state variables (like temperature, pressure, and volume).

### Step 2: Analyze Each Option
- **Option A: W (Work)**
- Work is a path function. The amount of work done depends on the specific path taken from the initial state to the final state. For example, in a PV diagram, different paths between the same two states will yield different amounts of work done.

- **Option B: Q (Heat)**
- Heat is also a path function. Similar to work, the amount of heat transferred depends on the process path taken. Different processes between the same two states can involve different amounts of heat transfer.

- **Option C: Q + W**
- According to the first law of thermodynamics, Q + W = ΔU (change in internal energy), which is a state function. Therefore, Q + W itself is not a path function; it is a state function because it depends only on the initial and final states of the system.

- **Option D: H - TS**
- H - TS represents the Gibbs free energy (G). Gibbs free energy is also a state function because it depends only on the state of the system and not on the path taken to reach that state.

### Step 3: Conclusion
From the analysis:
- **Path Functions**: A (W) and B (Q)
- **Not Path Functions**: C (Q + W) and D (H - TS)

Thus, the correct answer is:
**A and B are path functions.**