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

Options

A. (b), (c) and (d)
B. (a), (b) and (c)
C. (b) and (c)
D. (a) and (d)

Explanation

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

### Step-by-Step Solution:

1. **Understanding Path Functions**:
- A path function is a property that depends on the specific path taken during a process. In thermodynamics, work (W) and heat (Q) are examples of path functions because their values depend on how the process occurs, not just the initial and final states of the system.

2. **Analyzing Option (A) W**:
- Work (W) is a path function. The amount of work done by or on a system can vary depending on the process taken (e.g., isothermal, adiabatic). Therefore, **W is a path function**.

3. **Analyzing Option (B) Q**:
- Heat (Q) is also a path function. Similar to work, the amount of heat exchanged during a process depends on the path taken (e.g., how the temperature changes over time). Thus, **Q is a path function**.

4. **Analyzing Option (C) Q + W**:
- According to the first law of thermodynamics, the change in internal energy (ΔU) of a system is given by ΔU = Q + W. Since ΔU is a state function (it depends only on the initial and final states of the system), the sum Q + W is also a state function. Therefore, **Q + W is not a path function**.

5. **Analyzing Option (D) H - TS**:
- The expression H - TS represents the Gibbs free energy (G), which is another state function. It depends only on the state of the system and not on the path taken. Thus, **H - TS is not a path function**.

### Conclusion:
From the analysis, the path functions among the given options are:
- (A) W
- (B) Q

### Final Answer:
The correct options that are path functions are **(A) W and (B) Q**.

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