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It follows, for example, that the ratio of two extensive properties is an intensive property. To illustrate, consider a system having a certain mass, , and volume, . The density, is equal to mass (extensive) divided by volume (extensive): =.
Under STP, a reaction between three cubic meters of hydrogen gas and one cubic meter of nitrogen gas will produce about two cubic meters of ammonia.. The law of combining volumes states that when gases chemically react together, they do so in amounts by volume which bear small whole-number ratios (the volumes calculated at the same temperature and pressure).
An orientable manifold has infinitely many volume forms, since multiplying a volume form by a nowhere-vanishing real valued function yields another volume form. On non-orientable manifolds, one may instead define the weaker notion of a density. A volume form provides a means to define the integral of a function on a
An element of the density bundle at x is a function that assigns a volume for the parallelotope spanned by the n given tangent vectors at x. From the operational point of view, a density is a collection of functions on coordinate charts which become multiplied by the absolute value of the Jacobian determinant in the change of coordinates.
Volume, modulus of elasticity, distribution of forces, and yield strength affect the impact strength of a material. In order for a material or object to have a high impact strength, the stresses must be distributed evenly throughout the object. It also must have a large volume with a low modulus of elasticity and a high material yield strength. [7]
German mathematician Carl Friedrich Gauss said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics." Number theory also studies the natural, or whole, numbers. One of the central concepts in number theory is that of the prime number , and there are many questions about primes that appear simple but whose ...
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The theoretical molar yield is 2.0 mol (the molar amount of the limiting compound, acetic acid). The molar yield of the product is calculated from its weight (132 g ÷ 88 g/mol = 1.5 mol). The % yield is calculated from the actual molar yield and the theoretical molar yield (1.5 mol ÷ 2.0 mol × 100% = 75%). [citation needed]