Q.Choose the correct answer. A thermodynamic state function is a quantity

The key idea is that a state function depends only on the current state of the system, not on how it got there.

1. A state function’s value is determined solely by the system’s properties (like pressure, volume, temperature, and composition) at a given instant.
2. Therefore, its change between two states is independent of the path taken. This is the defining characteristic.
3. Options (i) and (iii) describe applications of certain quantities (e.g., heat, work), but work and heat themselves are path-dependent, not state functions. Option (iv) is too narrow — many state functions depend on more than just temperature.

Concept First: What Makes a Quantity a State Function?

In thermodynamics, we classify properties into two broad categories: state functions and path functions. The distinction is fundamental.

A state function is any property that has a unique value for a given thermodynamic state. Think of it like your current location on a map — the coordinates (latitude, longitude) describe exactly where you are, regardless of whether you walked, ran, or drove to get there. Similarly, properties like internal energy ($U$), enthalpy ($H$), entropy ($S$), pressure ($P$), volume ($V$), and temperature ($T$) are state functions. Their change between two states depends only on the initial and final states, not on the path taken.

A path function, on the other hand, depends on the route. Heat ($q$) and work ($w$) are classic examples. If you climb a mountain, the work you do depends on whether you take a steep trail or a gentle switchback — the change in altitude (a state function) is the same, but the effort (a path function) differs.

Now, let's examine each option carefully.

Step-by-Step Analysis

1. Option (i): "used to determine heat changes"

This is misleading. Heat changes ($q$) are path functions, not state functions. While we can use state functions like internal energy ($\Delta U$) to calculate heat under certain conditions (e.g., constant volume: $q_V = \Delta U$), the statement implies that state functions are tools for finding heat changes — which is too narrow and imprecise. Many state functions (like pressure or volume) aren't directly used for heat calculations. So this is not the defining characteristic.

2. Option (ii): "whose value is independent of path"

This is the textbook definition. A state function's value — or its change between two states — depends only on the initial and final states, not on the process connecting them. For example, $\Delta U$ for a system going from state A to state B is the same whether the process is reversible, irreversible, isothermal, or adiabatic. This is the core idea. This option is correct.

3. Option (iii): "used to determine pressure volume work"

Pressure-volume work is $W = -\int P \, dV$. While $P$ and $V$ are state functions, the work itself is a path function — it depends on how the pressure changes with volume along the path. So state functions are not used to determine work in a general sense; rather, work is calculated from the path. This option confuses the tool with the property.

4. Option (iv): "whose value depends on temperature only"

This is false. Many state functions depend on multiple variables. For an ideal gas, internal energy $U$ depends only on temperature, but enthalpy $H$ also depends only on temperature for an ideal gas. However, pressure $P$ depends on both temperature and volume, and entropy $S$ depends on temperature and volume (or pressure). So this is not a general property of state functions.

Final Answer