Question

Which one of the following is NOT a state function?

• A. Enthalpy
• B. Entropy
• C. Work
• D. Internal Energy

Hint:

Ask whether the quantity can be written purely from state variables like T, P, V, or whether it needs the exact process path.

Answer 1

The Correct Option is C

Step 1: Recall what a state function is.
A state function (or point function) is a thermodynamic property whose value depends only on the current state of the system, defined by variables such as temperature, pressure, and composition, and not on the path taken to reach that state. If a system moves from state 1 to state 2 by any two different processes, a state function changes by the same amount in both cases.

Step 2: Recall what a path function is.
A path function depends on the specific process, or path, followed between two states, not just on the states themselves. Two different processes connecting the same initial and final states can give completely different values for a path function. Heat (\(Q\)) and work (\(W\)) are the two classic path functions in thermodynamics.

Step 3: Analyze option (A), Enthalpy.
Enthalpy is defined as \(H = U + PV\), built entirely from state variables \(U\) (internal energy), \(P\) (pressure), and \(V\) (volume). Its value at a given state is fixed, so enthalpy is a state function. Incorrect choice for "NOT a state function".

Step 4: Analyze option (B), Entropy.
Entropy \(S\) is defined through \(dS = \frac{dQ_{rev}}{T}\) for a reversible path, but the resulting value of \(S\) itself depends only on the state, since the entropy change between two states is identical for every reversible or irreversible path connecting them; this path independence is exactly what makes entropy a valid state function. Incorrect choice.

Step 5: Analyze option (C), Work.
Work done on or by a system, \(W = \int P\,dV\) for a simple compressible system, depends on the exact path followed in a \(P\)-\(V\) diagram. Expanding a gas at constant pressure and expanding it in stages to the same final state give different areas under the curve, hence different amounts of work, even though the initial and final states are identical. Work is therefore a path function, not a state function. This is the correct choice.

Step 6: Analyze option (D), Internal Energy.
Internal energy \(U\) depends only on the state of the system (for an ideal gas, only on temperature). Even though the heat and work exchanged during a process can differ from path to path, their difference, \(\Delta U = Q - W\) (the first law), is always the same for a given pair of states. So internal energy is a state function. Incorrect choice.

Step 7: Final Answer.
Enthalpy, entropy, and internal energy are all defined purely by the state of the system, but work depends on the path taken.
\[ \boxed{\text{Work}} \]