Which Of The Following Is A State Function

The Question That Trips Up Almost Every Chemistry Student

Here's the thing — if you've ever sat through a thermodynamics lecture, you've probably heard the phrase "state function" thrown around like it's obvious. And then someone asks, "Which of the following is a state function?" and suddenly the room gets quiet.

I remember my first time. Half the class guessed. The professor listed a bunch of properties — pressure, volume, temperature, work, heat — and asked us to pick out the state functions. The other half looked like they were trying to remember if they'd studied the right chapter.

So let's cut through the confusion. Because this isn't just academic trivia. It's the kind of distinction that makes the rest of thermodynamics click — or not.

What Is a State Function, Really?

A state function is a property whose value doesn't depend on how you got there. It only cares about where you are.

Think of it like your bank account balance. Whether you deposited $100 in one transaction or five $20 deposits over a week, your final balance is the same. The path doesn't matter — only the starting and ending points.

In chemistry, state functions include things like energy, enthalpy, entropy, temperature, pressure, and volume. These are properties of the system itself, not of the process that changed the system.

Now here's where it gets tricky. Also, work and heat are not state functions. Because of that, they depend entirely on the path taken. If you compress a gas slowly versus slamming it down quickly, the work done is different — even if the gas ends up in the same state.

Why This Distinction Actually Matters

Get this wrong, and you'll stumble through half of thermodynamics. Here's why:

When you're calculating energy changes, enthalpy changes, or entropy changes, you can use simple subtraction. Final state minus initial state. That's the whole point of a state function — the path is irrelevant.

But work and heat? You can't just subtract. You need to know exactly what happened along the way. On the flip side, did the reaction happen at constant pressure? Constant volume? Was it reversible? Irreversible? All of that matters.

This is why the first law of thermodynamics is written the way it is: ΔU = q + w. Internal energy (a state function) equals heat plus work (both path functions). The change in energy depends only on the start and end states, but heat and work are the mechanisms that got you there.

How to Tell State Functions From Path Functions

Look at the Math

State functions have a special property in calculus: their differentials are exact. Here's the thing — this means you can integrate them without knowing the path. The integral of dU (internal energy) is just U_final - U_initial, no matter what.

Path functions have inexact differentials. You can't integrate them without specifying the path. The integral of dw (work) or dq (heat) depends on the specific process.

Check the Physical Meaning

Ask yourself: does this property belong to the system, or does it describe energy transfer?

Properties that belong to the system — like how much energy it contains, how hot it is, how much space it occupies — those are state functions.

Properties that describe energy in transit — like how much heat flowed, how much work was done — those are path functions.

Use the Common List

Here's what you need to memorize, because it comes up everywhere:

State functions: Internal energy (U), enthalpy (H), entropy (S), Gibbs free energy (G), temperature (T), pressure (P), volume (V), density, concentration, pH

Path functions: Work (w), heat (q)

The Classic Exam Question

Here's how these questions usually show up:

"Which of the following is a state function?"

A) Heat
B) Work
C) Internal energy
D) All of the above
E) None of the above

The answer is C. Practically speaking, internal energy is a state function. Heat and work are not.

But here's a trickier version you might see:

"Which of the following is a state function?"

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A) The work done by the system
B) The heat absorbed by the system
C) The enthalpy change of the system
D) The temperature of the surroundings

The answer here is C. Which means enthalpy change (ΔH) is a state function. The temperature of the surroundings might seem like it should be, but the question is asking about the system's properties, and the surroundings' temperature depends on the path of heat transfer.

Common Mistakes People Make

Confusing Heat and Temperature

I see this all the time. But students think because temperature is a state function, heat must be too. They're related, but they're not the same thing.

Temperature measures the average kinetic energy of molecules. Heat is energy transferred due to a temperature difference. One is a property of the system; the other is energy in motion.

Thinking Work Is Always a State Function

Some students reason: "Well, if I lift a book and put it on a shelf, the work done is mgh. That only depends on the height, not the path."

But that's gravitational work, not thermodynamic work. In thermodynamics, work usually means pressure-volume work (PΔV), and that absolutely depends on the path. Compress a gas quickly versus slowly, and you'll do different amounts of work even if the final volume is the same.

Mixing Up System and Surroundings

State functions describe the system. When a question asks about the surroundings, be careful. The surroundings' properties might depend on the path of energy transfer, even if they seem like they should be state functions.

Practical Tips for Getting This Right

Draw the Path

When you're unsure, sketch it out. Consider this: then draw two different paths between them. Draw the initial state and final state. If the property changes by the same amount along both paths, it's a state function.

Here's one way to look at it: if you have a gas going from state A to state B, you can take a direct path or go through an intermediate state C. If ΔU is the same for both paths, internal energy is a state function. (It is.

Use the "Only Care About Endpoints" Test

State functions only care about where you started and where you ended. If you can describe the change without mentioning the process, it's probably a state function.

"The internal energy increased by 50 J." That's a state function. Practically speaking, "50 J of heat flowed into the system. " That's a path function.

Remember the First Law

The first law of thermodynamics (ΔU = q + w) is actually a great reminder. Internal energy is a state function, so its change only depends on the endpoints. But heat and work are the path-dependent terms that add up to give you that change.

FAQ

Is enthalpy always a state function? Yes. Enthalpy (H = U + PV) is defined in terms of state functions, so it's automatically a state function. The change in enthalpy (ΔH) depends only on the initial and final states.

Can work ever be a state function? In general thermodynamics, no. Work depends on the path. Even so, in specific cases (like conservative force fields), you can define a potential energy that's a state function. But that's not the same as thermodynamic work.

Why is heat not a state function? Heat represents energy transfer, not a property of the system. The amount of heat transferred depends on the process, not just the initial and final states.

Is temperature a state function? Yes. Temperature is an intensive property of the system. It doesn't matter how the system reached that temperature — whether by heating slowly or quickly, the temperature is the same.

What about Gibbs free energy? Gibbs free energy (G = H - TS) is a state function because it's defined in terms of other state functions. Changes in G depend only on the initial and final states.

The Bottom Line

Here's what I want you to remember: state functions are about what the system is like*. Path functions are about what happened to the system*.

Energy, enthalpy, entropy, temperature, pressure, volume — these describe the system's condition. Heat and work describe the process.

And honestly? Once you internalize that distinction, a lot of thermodynamics stops feeling like memorization and starts feeling like logic.