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 options are state functions, we need to understand the difference between state functions and path functions.

**Step 1: Define State Functions and Path Functions**
- State functions are properties that depend only on the current state of the system, regardless of how it got there. Examples include internal energy (U), enthalpy (H), entropy (S), pressure (P), volume (V), and temperature (T).
- Path functions depend on the specific path taken to reach a particular state. They are not solely determined by the initial and final states. Examples include heat (q) and work (w).

**Step 2: Analyze Each Option**
1. **U + PV**: This expression represents the Helmholtz free energy (A) when rearranged. Since U (internal energy) and PV (pressure-volume work) are both state functions, their sum is also a state function.
2. **S**: Entropy (S) is a classic example of a state function. It depends only on the state of the system.
3. **q**: Heat (q) is a path function because it depends on how the energy is transferred to or from the system.
4. **w**: Work (w) is also a path function as it depends on the process taken to do the work.
5. **H - TS**: This expression represents the Gibbs free energy (G). Since both H (enthalpy) and TS (temperature times entropy) are state functions, their difference is also a state function.

**Step 3: Conclusion**
Based on the analysis:
- State functions: (i) U + PV, (ii) S, (v) H - TS
- Path functions: (iii) q, (iv) w

Thus, the state functions among the given options are:
- (i) U + PV
- (ii) S
- (v) H - TS

**Final Answer:**
The state functions are (i), (ii), and (v).

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