law of multiple proportions

Examples of law of multiple proportions in the following topics:

• The Law of Multiple Proportions

  • The law of multiple proportions states that elements combine in small whole number ratios to form compounds.
  • The law of multiple proportions, also known as Dalton's law, was proposed by the English chemist and meteorologist John Dalton in his 1804 work, A New System of Chemical Philosophy.
  • The law, which was based on Dalton's observations of the reactions of atmospheric gases, states that when elements form compounds, the proportions of the elements in those chemical compounds can be expressed in small whole number ratios.
  • Dalton's law of multiple proportions is part of the basis for modern atomic theory, along with Joseph Proust's law of definite composition (which states that compounds are formed by defined mass ratios of reacting elements) and the law of conservation of mass that was proposed by Antoine Lavoisier.
  • These laws paved the way for our current understanding of atomic structure and composition, including concepts like molecular or chemical formulas.

• The Law of Definite Composition

  • The law of definite composition states that chemical compounds are composed of a fixed ratio of elements as determined by mass.
  • French chemist Joseph Proust proposed the law of definite composition or proportions based on his experiments conducted between 1798 and 1804 on the elemental composition of water and copper carbonate.
  • Dalton's law of multiple proportions expanded on the law of definite composition to postulate that, in situations in which elements can combine to form multiple combinations, the ratio of the elements in those compounds can be expressed as small whole numbers.
  • There are some exceptions to the law of definite composition.
  • This video examines the law of definite proportions and the law of multiple proportions.

• Hooke's Law

  • Hooke's law of elasticity is an approximation that states that the extension of a spring is directly proportional to the load applied to it.
  • It states: the extension of a spring is in direct proportion with the load applied to it .
  • In simple terms, Hooke's law says that stress is directly proportional to strain.
  • It's possible for multiple springs to act on the same point.
  • The extension of the spring is linearly proportional to the force.

• Gauss's Law

  • Gauss's law is a law relating the distribution of electric charge to the resulting electric field.
  • Gauss's law, also known as Gauss's flux theorem, is a law relating the distribution of electric charge to the resulting electric field.
  • It is one of the four Maxwell's equations which form the basis of classical electrodynamics, the other three being Gauss's law for magnetism, Faraday's law of induction, and Ampère's law with Maxwell's correction.
  • In words, Gauss's law states that: The net outward normal electric flux through any closed surface is proportional to the total electric charge enclosed within that closed surface.
  • Gauss's law has a close mathematical similarity with a number of laws in other areas of physics, such as Gauss's law for magnetism and Gauss's law for gravity.

• The Law of Universal Gravitation

  • Objects with mass feel an attractive force that is proportional to their masses and inversely proportional to the square of the distance.
  • Theorizing that this force must be proportional to the masses of the two objects involved, and using previous intuition about the inverse-square relationship of the force between the earth and the moon, Newton was able to formulate a general physical law by induction.
  • The Law of Universal Gravitation states that every point mass attracts every other point mass in the universe by a force pointing in a straight line between the centers-of-mass of both points, and this force is proportional to the masses of the objects and inversely proportional to their separation This attractive force always points inward, from one point to the other.
  • It wasn't until Henry Cavendish's verification of the gravitational constant that the Law of Universal Gravitation received its final algebraic form:
  • The force is proportional to the masses and inversely proportional to the square of the distance.

• Equations of State

  • It was first stated by Émile Clapeyron in 1834 as a combination of Boyle's law and Charles' law.
  • Boyle's law states that pressure P and volume V of a given mass of confined gas are inversely proportional:
  • while Charles' law states that volume of a gas is proportional to the absolute temperature T of the gas at constant pressure
  • where C is a constant which is directly proportional to the amount of gas, n (representing the number of moles).
  • Therefore, we derive a microscopic version of the ideal gas law

• Faraday's Law of Induction and Lenz' Law

  • First, EMF is directly proportional to the change in flux Δ.
  • This relationship is known as Faraday's law of induction.
  • The minus sign in Faraday's law of induction is very important.
  • Lenz' law is a manifestation of the conservation of energy.
  • Express the Faraday’s law of induction in a form of equation

• Charles' and Gay-Lussac's Law: Temperature and Volume

  • Charles' and Gay-Lussac's Law states that at constant pressure, temperature and volume are directly proportional.
  • Charles' Law describes the relationship between the volume and temperature of a gas.
  • This law states that at constant pressure, the volume of a given mass of an ideal gas increases or decreases by the same factor as its temperature (in Kelvin); in other words, temperature and volume are directly proportional.
  • A visual expression of Charles' and Gay-Lussac's Law is shown in a graph of the volume of one mole of an ideal gas as a function of its temperature at various constant pressures.
  • This extrapolation of Charles' Law was the first evidence of the significance of this temperature.

• Introduction to inference for a single proportion

  • Chapter 6 introduces inference in the setting of categorical data.
  • What proportion of the American public approves of the job the Supreme Court is doing?
  • The Pew Research Center conducted a poll about support for the 2010 health care law, and they used two forms of the survey question.
  • For example, sample proportions are well characterized by a nearly normal distribution when certain conditions are satisfied, making it possible to employ the usual confidence interval and hypothesis testing tools.
  • According to a New York Times / CBS News poll in June 2012, only about 44% of the American public approves of the job the Supreme Court is doing. 1 This poll included responses of 976 adults.

• Addition, Subtraction, and Multiplication

  • The multiplication of two complex numbers is defined by the following formula:
  • The preceding definition of multiplication of general complex numbers follows naturally from this fundamental property of the imaginary unit.
  • $(a + bi)(c + di) = ac + bci + adi + bidi$ (by the distributive law)
  • = $ac + bidi + bci + adi$ (by the commutative law of addition)
  • = $ac + bdi^2 + (bc + ad)i$ (by the commutative law of multiplication)