Third law of thermodynamics

Key takeaways

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

Reference excerpt

The third law of thermodynamics states that the entropy of a closed system at thermodynamic equilibrium approaches a constant value when its temperature approaches absolute zero. This constant value cannot depend on any other parameters characterizing the system, such as pressure or applied magnetic field. At absolute zero (zero kelvin) the system must be in a state with the minimum possible energy. Entropy is related to the number of accessible microstates, and there is typically one unique state (called the ground state) with minimum energy. In such a case, the entropy at absolute zero will be exactly zero. If the system does not have a well-defined order (if its order is glassy, for example), then there may remain some finite entropy as the system is brought to very low temperatures, either because the system becomes locked into a configuration with non-minimal energy or because the minimum energy state is non-unique. The constant value is called the residual entropy of the system.

Formulations The third law has many formulations, some more general than others, some equivalent, and some neither more general nor equivalent. The Planck statement applies only to perfect crystalline substances:

As temperature falls to zero, the entropy of any pure crystalline substance tends to a universal constant. That is, lim T → 0 S = S 0 {\displaystyle \lim _{T\to 0}S=S_{0}} , where S 0 {\displaystyle S_{0}} is a universal constant that applies for all possible crystals, of all possible sizes, in all possible external constraints. So it can be taken as zero, giving lim T → 0 S = 0 {\displaystyle \lim _{T\to 0}S=0} . The Nernst statement concerns thermodynamic processes at a fixed, low temperature, for condensed systems, which are liquids and solids:

The entropy change associated with any condensed system undergoing a reversible isothermal process approaches zero as the temperature at which it is performed approaches 0 K. That is, lim T → 0 S ( T , X 1 ) − S ( T , X 2 ) = 0 {\displaystyle \lim _{T\to 0}S(T,X_{1})-S(T,X_{2})=0} , or equivalently,

At absolute zero, the entropy change becomes independent of the process path. That is,

∀ x , lim T → 0 | S ( T , x ) − S ( T , x + Δ x ) | → 0 {\displaystyle \forall x,\lim _{T\to 0}|S(T,x)-S(T,x+\Delta x)|\to 0}

where Δ x {\displaystyle \Delta x} represents a change in the state variable x {\displaystyle x} . The unattainability principle of Nernst:

It is impossible for any process, no matter how idealized, to reduce the entropy of a system to its absolute-zero value in a finite number of operations. This principle implies that cooling a system to absolute zero would require an infinite number of steps or an infinite amount of time. The statement in adiabatic accessibility:

It is impossible to start from a state of positive temperature, and adiabatically reach a state with zero temperature. The Einstein statement:

The entropy of any substance approaches a finite value as the temperature approaches absolute zero. That is, ∀ x , lim T → 0 S ( T , x ) → S 0 ( x ) {\textstyle \forall x,\lim _{T\to 0}S(T,x)\rightarrow S_{0}(x)} where S {\displaystyle S} is the entropy, the zero-point entropy S 0 ( x ) {\displaystyle S_{0}(x)} is finite-valued, T {\displaystyle T} is the temperature, and x {\displaystyle x} represents other relevant state variables. This implies that the heat capacity C ( T , x ) {\displaystyle C(T,x)} of a substance must (uniformly) vanish at absolute zero, as otherwise the entropy S = ∫ 0 T 1 C ( T , x ) d T T {\displaystyle S=\int _{0}^{T_{1}}{\frac {C(T,x)dT}{T}}} would diverge.

… excerpt ends here. Continue reading the full article.

Illustrations

Worked examples

Example 1 — a first encounter with Third law of thermodynamics

Start with the simplest possible case. Write down what Third law of thermodynamics claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, 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 Third law of thermodynamics 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 Third law of thermodynamics 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 Third law of thermodynamics

In research: Third law of thermodynamics appears in physics 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 Third law of thermodynamics 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: Third law of thermodynamics is common in secondary-school and first-year university syllabi. It links to neighbouring topics Laws of thermodynamics, so understanding it makes those chapters shorter.
In everyday life: Look for Third law of thermodynamics 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.

How to study Third law of thermodynamics in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Third law of thermodynamics 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 Third law of thermodynamics out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Third law of thermodynamics in simple terms?

The third law of thermodynamics states that the entropy of a closed system at thermodynamic equilibrium approaches a constant value when its temperature approaches absolute zero. This constant value cannot depend on any other parameters characterizing the system, such as pressure or applied magneti…

Why does Third law of thermodynamics matter?

Because it connects several physics 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 Third law of thermodynamics?

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 Third law of thermodynamics.