mathematics

Nernst heat theorem

Nernst heat theorem is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Nernst heat theorem rather than just read about it. In short: The Nernst heat theorem was formulated by Walther Nernst early in the twentieth century and was used in the development of the third law of thermodynamics. The theorem The Nernst heat theorem says that as absolute zero is approached, the entropy change ΔS for a chemical or physical transformation approaches 0.

Key takeaways

Nernst heat theorem belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Nernst heat theorem to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Nernst heat theorem from memory before moving on to harder problems.

Reference excerpt

The Nernst heat theorem was formulated by Walther Nernst early in the twentieth century and was used in the development of the third law of thermodynamics.

The theorem The Nernst heat theorem says that as absolute zero is approached, the entropy change ΔS for a chemical or physical transformation approaches 0. This can be expressed mathematically as follows:

lim T → 0 Δ S = 0 {\displaystyle \lim _{T\to 0}\Delta S=0}

The above equation is a modern statement of the theorem. Nernst often used a form that avoided the concept of entropy.

Another way of looking at the theorem is to start with the definition of the Gibbs free energy (G), G = H − T S {\displaystyle G=H-TS} , where H stands for enthalpy. For a change from reactants to products at constant temperature and pressure the equation becomes Δ G = Δ H − T Δ S {\displaystyle \Delta G=\Delta H-T\Delta S} . In the limit of T = 0 the equation reduces to just ΔG = ΔH, as illustrated in the figure shown here, which is supported by experimental data. However, it is known from thermodynamics that the slope of the ΔG curve is −ΔS. Since the slope shown here reaches the horizontal limit of 0 as T → 0 then the implication is that ΔS → 0, which is the Nernst heat theorem. The significance of the Nernst heat theorem is that it was later used by Max Planck to give the third law of thermodynamics, which is that the entropy of all pure, perfectly crystalline homogeneous materials in complete internal equilibrium is 0 at absolute zero.

Illustrations

Nernst heat theorem: Enthalpy and free energy both have a slope of zero and become equal as temperature approaches absolute zero — Enthalpy and free energy both have a slope of zero and become equal as temperature approaches absolute zero

Worked examples

Example 1 — a first encounter with Nernst heat theorem

Start with the simplest possible case. Write down what Nernst heat theorem claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Nernst heat theorem before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Nernst heat theorem ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Nernst heat theorem

In research: Nernst heat theorem appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Nernst heat theorem in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Nernst heat theorem is common in secondary-school and first-year university syllabi. It links to neighbouring topics Thermochemistry, Walther Nernst, so understanding it makes those chapters shorter.
In everyday life: Look for Nernst heat theorem outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Nernst heat theorem in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Nernst heat theorem means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Nernst heat theorem out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Nernst heat theorem in simple terms?

The Nernst heat theorem was formulated by Walther Nernst early in the twentieth century and was used in the development of the third law of thermodynamics. The theorem The Nernst heat theorem says that as absolute zero is approached, the entropy change ΔS for a chemical or physical transformation a…

Why does Nernst heat theorem matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Nernst heat theorem?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Nernst heat theorem.