Empirical law in the context of Reproducibility

⭐ Core Definition: Empirical law

Scientific laws or laws of science are statements, based on repeated experiments or observations, that describe or predict a range of natural phenomena. The term law has diverse usage in many cases (approximate, accurate, broad, or narrow) across all fields of natural science (physics, chemistry, astronomy, geoscience, biology). Laws are developed from data and can be further developed through mathematics; in all cases they are directly or indirectly based on empirical evidence. It is generally understood that they implicitly reflect, though they do not explicitly assert, causal relationships fundamental to reality, and are discovered rather than invented.

Scientific laws summarize the results of experiments or observations, usually within a certain range of application. In general, the accuracy of a law does not change when a new theory of the relevant phenomenon is worked out, but rather the scope of the law's application, since the mathematics or statement representing the law does not change. As with other kinds of scientific knowledge, scientific laws do not express absolute certainty, as mathematical laws do. A scientific law may be contradicted, restricted, or extended by future observations.

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⭐ Core Definition: Empirical law
Empirical law in the context of Laws of thermodynamics
Empirical law in the context of Spring constant
Empirical law in the context of Zipf's law

Empirical law in the context of Laws of thermodynamics

The laws of thermodynamics are a set of scientific laws which define a group of physical quantities, such as temperature, energy, and entropy, that characterize thermodynamic systems in thermodynamic equilibrium. The laws also use various parameters for thermodynamic processes, such as thermodynamic work and heat, and establish relationships between them. They state empirical facts that form a basis of precluding the possibility of certain phenomena, such as perpetual motion. In addition to their use in thermodynamics, they are important fundamental laws of physics in general and are applicable in other natural sciences.

Traditionally, thermodynamics has recognized three fundamental laws, simply named by an ordinal identification, the first law, the second law, and the third law. A more fundamental statement was later labelled as the zeroth law after the first three laws had been established.

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Empirical law in the context of Spring constant

In physics, Hooke's law is an empirical law which states that the force ( $F$ ) needed to extend or compress a spring by some distance ( $x$ ) scales linearly with respect to that distance—that is, $F s = kx$ , where $k$ is a constant factor characteristic of the spring (i.e., its stiffness), and $x$ is small compared to the total possible deformation of the spring.

The law is named after 17th-century British physicist Robert Hooke. He first stated the law in 1676 as a Latin anagram. He published the solution of his anagram in 1678 as: ut tensio, sic vis ("as the extension, so the force" or "the extension is proportional to the force"). Hooke states in the 1678 work that he was aware of the law since 1660. It is the fundamental principle behind the spring scale, the manometer, the galvanometer, and the balance wheel of the mechanical clock.

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Empirical law in the context of Zipf's law

Zipf's law (/zɪf/) is an empirical law stating that when a set of measured values is sorted in decreasing order, the value of the $n$ -th entry is often approximately inversely proportional to $n$ .

The best-known instance of Zipf’s law applies to the frequency distribution of words in a text or corpus of natural language:

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Empirical law in the context of Reproducibility

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⭐ Core Definition: Empirical law

Empirical law in the context of Laws of thermodynamics

Empirical law in the context of Spring constant

Empirical law in the context of Zipf's law