In thermodynamics, which of the following combinations represent state functions? 1. q + w 2. q (heat exchanged) 3. w (work done) 4. H − T S. Select the correct answer using the code given below.

Introduction / Context:

Chemical thermodynamics distinguishes between state functions and path functions. State functions depend only on the initial and final states of a system, while path functions depend on the specific way the process is carried out. Examinations often test whether you can correctly classify common thermodynamic quantities such as heat, work, internal energy and Gibbs free energy. This question asks which of the given combinations are state functions.

Given Data / Assumptions:

• q denotes heat exchanged between system and surroundings.
• w denotes work done by or on the system.
• q + w is related to change in internal energy.
• H is enthalpy, T is temperature and S is entropy, so H − T S represents Gibbs free energy G.

Concept / Approach:

According to the first law of thermodynamics, the change in internal energy ΔU of a system is given by ΔU = q + w (for a particular sign convention). Internal energy U is a state function because it depends only on the state of the system. Heat q and work w individually are not state functions; they depend on the path taken between initial and final states. Gibbs free energy G is defined as G = H − T S, where enthalpy H, temperature T and entropy S are all state functions. Any combination formed from state functions by algebraic addition, subtraction or multiplication by constants is also a state function.

Step-by-Step Solution:

Verification / Alternative check:

Think of a gas expanding from volume V1 to volume V2. If it expands reversibly, the work and heat have certain values. If it expands irreversibly (for example, free expansion), the values of q and w change, but the initial and final states are the same, so ΔU and ΔG depend only on state and remain unchanged. This confirms that q and w are path dependent, whereas q + w (internal energy change) and H − T S (Gibbs free energy) are state functions.

Why Other Options Are Wrong:

Option B: 1, 2 and 4 incorrectly includes heat q as a state function.

Option C: 2, 3 and 4 incorrectly includes both q and w as state functions.

Option D: 1 only ignores the fact that H − T S is also a state function representing Gibbs free energy.

Common Pitfalls:

A frequent misconception is to assume that any commonly used thermodynamic quantity is a state function. Students often forget that heat and work are process quantities, not properties of state. Remember that any quantity expressible solely in terms of state variables (such as P, V, T, U, H, S) is a state function, while quantities that require knowledge of the path are not.

Final Answer:

The state functions among the given options are 1 and 4 only.