Select the state functions among the following.
(i) U + PV (ii) S
(iii) q (iv) w
H - TS

Options

A. (iii), (iv) and (v) only
B. (i), (ii) and (v) Only
C. (iii) and (iv) Only
D. (ii), (iii), (iv) and (v) Only

Answer

To determine which of the given functions are state functions, we need to understand the definition of state functions and path functions.

### Step-by-Step Solution:

1. **Understanding State Functions**:
- State functions are properties that depend only on the current state of the system, not on how the system arrived at that state. Examples include internal energy (U), enthalpy (H), entropy (S), and Gibbs free energy (G).

2. **Analyze Each Option**:
- **(i) U + PV**:
- This expression is equal to the enthalpy (H). Since enthalpy is a state function, U + PV is also a state function.

- **(ii) S (Entropy)**:
- Entropy is a well-known state function. Its value depends only on the state of the system and not on the path taken to reach that state.

- **(iii) q (Heat)**:
- Heat is a path function. The amount of heat transferred depends on the specific process or path taken between two states, so it is not a state function.

- **(iv) w (Work)**:
- Work is also a path function. The work done depends on the path taken to go from one state to another, making it not a state function.

- **(v) H - TS**:
- This expression represents Gibbs free energy (G). Gibbs free energy is a state function as it depends only on the initial and final states of the system.

3. **Conclusion**:
- From the analysis, the state functions among the given options are:
- (i) U + PV (which is H)
- (ii) S
- (v) H - TS (which is G)

### Final Answer:
The state functions are:
- (i) U + PV
- (ii) S
- (v) H - TS