physics

Zeroth law of thermodynamics

Zeroth law of thermodynamics is a physics 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 Zeroth law of thermodynamics rather than just read about it. In short: The zeroth law of thermodynamics is one of the four principal laws of thermodynamics. It provides an independent definition of temperature without reference to entropy, which is defined in the second law.

Key takeaways

Zeroth 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 Zeroth law of thermodynamics to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Zeroth law of thermodynamics from memory before moving on to harder problems.

Reference excerpt

The zeroth law of thermodynamics is one of the four principal laws of thermodynamics. It provides an independent definition of temperature without reference to entropy, which is defined in the second law. The law was established by Ralph H. Fowler in the 1930s, long after the first, second, and third laws had been widely recognized. The zeroth law states that if two thermodynamic systems are both in thermal equilibrium with a third system, then the two systems are in thermal equilibrium with each other. Two systems are said to be in thermal equilibrium if they are linked by a wall permeable only to heat, and they do not change over time. Another formulation by James Clerk Maxwell is "All heat is of the same kind". Another statement of the law is "All diathermal walls are equivalent". The zeroth law is important for the mathematical formulation of thermodynamics. It makes the relation of thermal equilibrium between systems an equivalence relation, which can represent equality of some quantity associated with each system. A quantity that is the same for two systems, if they can be placed in thermal equilibrium with each other, is a scale of temperature. The zeroth law is needed for the definition of such scales, and justifies the use of practical thermometers.

Equivalence relation A thermodynamic system is by definition in its own state of internal thermodynamic equilibrium, that is to say, there is no change in its observable state (i.e. macrostate) over time and no flows occur in it. One precise statement of the zeroth law is that the relation of thermal equilibrium is an equivalence relation on pairs of thermodynamic systems. In other words, the set of all systems each in its own state of internal thermodynamic equilibrium may be divided into subsets in which every system belongs to one and only one subset, and is in thermal equilibrium with every other member of that subset, and is not in thermal equilibrium with a member of any other subset. This means that a unique "tag" can be assigned to every system, and if the "tags" of two systems are the same, they are in thermal equilibrium with each other, and if different, they are not. This property is used to justify the use of empirical temperature as a tagging system. Empirical temperature provides further relations of thermally equilibrated systems, such as order and continuity with regard to "hotness" or "coldness", but these are not implied by the standard statement of the zeroth law. If it is defined that a thermodynamic system is in thermal equilibrium with itself (i.e., thermal equilibrium is reflexive), then the zeroth law may be stated as follows:

If a body C, be in thermal equilibrium with two other bodies, A and B, then A and B are in thermal equilibrium with one another. This statement asserts that thermal equilibrium is a left-Euclidean relation between thermodynamic systems. If we also define that every thermodynamic system is in thermal equilibrium with itself, then thermal equilibrium is also a reflexive relation. Binary relations that are both reflexive and Euclidean are equivalence relations. Thus, again implicitly assuming reflexivity, the zeroth law is therefore often expressed as a right-Euclidean statement:

If two systems are in thermal equilibrium with a third system, then they are in thermal equilibrium with each other. One consequence of an equivalence relationship is that the equilibrium relationship is symmetric: If A is in thermal equilibrium with B, then B is in thermal equilibrium with A. Thus, the two systems are in thermal equilibrium with each other, or they are in mutual equilibrium. Another consequence of equivalence is that thermal equilibrium is described as a transitive relation:

If A is in thermal equilibrium with B and if B is in thermal equilibrium with C, then A is in thermal equilibrium with C. A reflexive, transitive relation does not guarantee an equivalence relationship. For the above statement to be true, both reflexivity and symmetry must be implicitly assumed. It is the Euclidean relationships which apply directly to thermometry. An ideal thermometer is a thermometer which does not measurably change the state of the system it is measuring. Assuming that the unchanging reading of an ideal thermometer is a valid tagging system for the equivalence classes of a set of equilibrated thermodynamic systems, then the systems are in thermal equilibrium, if a thermometer gives the same reading for each system. If the system are thermally connected, no subsequent change in the state of either one can occur. If the readings are different, then thermally connecting the two systems causes a change in the states of both systems. The zeroth law provides no information regarding this final reading.

… excerpt ends here. Continue reading the full article.

Illustrations

Worked examples

Example 1 — a first encounter with Zeroth law of thermodynamics

Start with the simplest possible case. Write down what Zeroth 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 Zeroth 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 Zeroth 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 Zeroth law of thermodynamics

In research: Zeroth 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 Zeroth 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: Zeroth 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 Zeroth 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.

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How to study Zeroth law of thermodynamics in 20 minutes

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

Frequently asked questions

What is Zeroth law of thermodynamics in simple terms?

Why does Zeroth 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 Zeroth 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 Zeroth law of thermodynamics.