physics

Theorem of corresponding states

Theorem of corresponding states 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 Theorem of corresponding states rather than just read about it. In short: According to van der Waals, the theorem of corresponding states (or principle/law of corresponding states) indicates that all fluids, when compared at the same reduced temperature and reduced pressure, have approximately the same compressibility factor and all deviate from ideal gas behavior to about the same degree. Material constants that vary for each type of material are eliminated, in a recast reduced form of a…

Key takeaways

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

Reference excerpt

According to van der Waals, the theorem of corresponding states (or principle/law of corresponding states) indicates that all fluids, when compared at the same reduced temperature and reduced pressure, have approximately the same compressibility factor and all deviate from ideal gas behavior to about the same degree. Material constants that vary for each type of material are eliminated, in a recast reduced form of a constitutive equation. The reduced variables are defined in terms of critical variables. The principle originated with the work of Johannes Diderik van der Waals in about 1873 when he used the critical temperature and critical pressure to derive a universal property of all fluids that follow the van der Waals equation of state. It predicts a value of 3 / 8 = 0.375 {\displaystyle 3/8=0.375} that is found to be an overestimate when compared to real gases. Edward A. Guggenheim used the phrase "Principle of Corresponding States" in an oft-cited paper to describe the phenomenon where different systems have very similar behaviors when near a critical point. There are many examples of non-ideal gas models which satisfy this theorem, such as the van der Waals model, the Dieterici model, and so on, that can be found on the page on real gases.

Compressibility factor at the critical point The compressibility factor at the critical point, which is defined as Z c = P c v c μ R T c {\displaystyle Z_{c}={\frac {P_{c}v_{c}\mu }{RT_{c}}}} , where the subscript c {\displaystyle c} indicates physical quantities measured at the critical point, is predicted to be a constant independent of substance by many equations of state. The table below for a selection of gases uses the following conventions:

T c {\displaystyle T_{c}} : critical temperature [K]

P c {\displaystyle P_{c}} : critical pressure [Pa]

v c {\displaystyle v_{c}} : critical specific volume [m3⋅kg−1]

R {\displaystyle R} : gas constant (8.314 J⋅K−1⋅mol−1)

μ {\displaystyle \mu } : Molar mass [kg⋅mol−1]

See also Van der Waals equation Equation of state Compressibility factors Johannes Diderik van der Waals equation Noro-Frenkel law of corresponding states

References

External links Properties of Natural Gases. Includes a chart of compressibility factors versus reduced pressure and reduced temperature (on last page of the PDF document) Theorem of corresponding states on SklogWiki.

Illustrations

Worked examples

Example 1 — a first encounter with Theorem of corresponding states

Start with the simplest possible case. Write down what Theorem of corresponding states 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 Theorem of corresponding states 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 Theorem of corresponding states 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 Theorem of corresponding states

In research: Theorem of corresponding states 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 Theorem of corresponding states 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: Theorem of corresponding states is common in secondary-school and first-year university syllabi. It links to neighbouring topics Continuum mechanics, Engineering thermodynamics, Johannes Diderik van der Waals, so understanding it makes those chapters shorter.
In everyday life: Look for Theorem of corresponding states 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 Theorem of corresponding states in 20 minutes

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

Frequently asked questions

What is Theorem of corresponding states in simple terms?

Why does Theorem of corresponding states 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 Theorem of corresponding states?

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 Theorem of corresponding states.