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However, these units are not quite practical when dealing with atoms or molecules of gases, liquids or solids at room temperature and atmospheric pressure, because the resulting numbers are extremely large (on the order of 10 20). Using the number density of an ideal gas at 0 °C and 1 atm as a yardstick: n 0 = 1 amg = 2.686 7774 × 10 25 m − ...
is the static pressure [M 1 L −1 T −2], is the specific gas constant [L 2 T −2 θ −1] (287.05 J/(kg K) for air), is the density [M 1 L −3]. If the temperature is increased, but the volume kept constant, then the Knudsen number (and the mean free path) doesn't change (for an ideal gas). In this case, the density stays the same.
Thus a relative density less than one relative to water means that the substance floats in water. The density of a material varies with temperature and pressure. This variation is typically small for solids and liquids but much greater for gases. Increasing the pressure on an object decreases the volume of the object and thus increases its density.
In chemistry, the mass concentration ρ i (or γ i) is defined as the mass of a constituent m i divided by the volume of the mixture V. [1]= For a pure chemical the mass concentration equals its density (mass divided by volume); thus the mass concentration of a component in a mixture can be called the density of a component in a mixture.
1234 = number of parts in all partitions of 30 into distinct parts, [84] smallest whole number containing all numbers from 1 to 4; 1235 = excluding duplicates, contains the first four Fibonacci numbers [228] 1236 = 617 + 619: sum of twin prime pair [229] 1237 = prime of the form 2p-1; 1238 = number of partitions of 31 that do not contain 1 as a ...
In 1930 Schnirelmann used these ideas in conjunction with the Brun sieve to prove Schnirelmann's theorem, [1] [2] that any natural number greater than 1 can be written as the sum of not more than C prime numbers, where C is an effectively computable constant: [6] Schnirelmann obtained C < 800000. [7]
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The mean free path was also uncertain. Nevertheless, Loschmidt arrived at a diameter of about one nanometre, of the correct order of magnitude. Loschmidt's estimated data for air give a value of n 0 = 1.81 × 10 24 m −3. Eight years later, Maxwell was citing a figure of "about 19 million million million" per cm 3, or 1.9 × 10 25 m −3. [4]