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The variable y is directly proportional to the variable x with proportionality constant ~0.6. The variable y is inversely proportional to the variable x with proportionality constant 1. In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio.
Ohm's law states that the electric current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, [1] one arrives at the three mathematical equations used to describe this relationship: [2]
Faraday discovered that when the same amount of electric current is passed through different electrolytes connected in series, the masses of the substances deposited or liberated at the electrodes are directly proportional to their respective chemical equivalent/equivalent weight (E). [3]
The fact that the energy density of the box containing radiation is proportional to can be derived using thermodynamics. [ 32 ] [ 15 ] This derivation uses the relation between the radiation pressure p and the internal energy density u {\displaystyle u} , a relation that can be shown using the form of the electromagnetic stress–energy tensor .
In simple words, we can say that the partial pressure of a gas in vapour phase is directly proportional to the mole fraction of a gas in solution. An example where Henry's law is at play is the depth-dependent dissolution of oxygen and nitrogen in the blood of underwater divers that changes during decompression, going to decompression sickness.
[1]: 117 The formula above is known as the Langevin paramagnetic equation. Pierre Curie found an approximation to this law that applies to the relatively high temperatures and low magnetic fields used in his experiments. As temperature increases and magnetic field decreases, the argument of the hyperbolic tangent decreases. In the Curie regime,
This equation does not contain the temperature and so is not what became known as Charles's Law. Gay-Lussac's value for k (1 ⁄ 2.6666), was identical to Dalton's earlier value for vapours and remarkably close to the present-day value of 1 ⁄ 2.7315. Gay-Lussac gave credit for this equation to unpublished statements by his fellow Republican ...
The quantity grows at a rate directly proportional to its present size. For example, when it is 3 times as big as it is now, it will be growing 3 times as fast as it is now. In more technical language, its instantaneous rate of change (that is, the derivative) of a quantity with respect to an independent variable is proportional to the quantity ...