Speed of gas molecules

EXAMPLE 4.9 Sample exercise Calculating the root mean square speed of gas molecules... 

How does the root mean square speed of gas molecules vary with temperature Illustrate this relationship by plotting the root mean square speed of N, as a function of temperature from T = 100 I< to T = 300 K. ... 

Table 1.4 The average speeds of gas molecules at 273.15 K, given in order of increasing molecular mass. The speeds c are in fact root-mean-square speeds, obtained by squaring each velocity, taking their mean and then taking the square root of the sum...

FIGURE 4.26 The average speeds of gas molecules at 25°C in meters per second. The gases are some of the components of air hydrogen is included to show that the average speed of light molecules is much greater than that of heavy molecules. 

Thus it is possible to compute the average speed of gas molecules merely from a knowledge of the pressure p and gas density p. For hydrogen under standard conditions, C = 1696 m/s, approximately the speed of a bullet. This simple derivation is reasonably accurate, even though the assumption is made that all molecules are traveling at the same velocity. Often simplifying assumptions permit the parameters in an equation to be identified, even if the values of the constants may be somewhat inaccurate. 

Mean Free Path of a Pure Gas Let us start with the simplest case, a particle suspended in a pure gas B. If we are interested in characterizing the nature of the suspending gas relative to the particle, the mean free path that appears in the definition of the Knudsen number is kBB. The subscript denotes that we are interested in collisions of molecules of B with other molecules of B. Ordinarily, air will be the predominant vapor species in such a situation. The mean free path A.br has been defined as the average distance traveled by a B molecule between collisions with other B molecules. The mean speed of gas molecules of B, cB is (Moore 1962, p. 238)... 

The Maxwell distribution describes the distribution of the speeds of gas molecules at a given temperature ... 

A Figure 10.13 Distribution of molecular speeds for nitrogen gas. (a) The effect of temperature on molecular speed. The relative area under the curve for a range of speeds gives the relative fraction of molecules that have those speeds, (b) Position of most probable (Ump), average (Uav), and root-mean-square (u,rns) speeds of gas molecules. The data shown here are for nitrogen gas at 0°C. 

Calculating the rms speed of gas molecules Given the molecular weight and temperature of a gas, calculate the rms molecular speed. (EXAMPLE 5.12)... 

To interpret sieve data, graphical and statistical methods of data presentation are used. The distribution curve that is widely used in industrial practice was developed by Rosin, Rammler, Sperling, and Bennett in the 1930s (Rosin, Rammler, Sperling, 1997 Rosin and Rammler, 1933 Bennett, 1936). They found out that the size distribution of coal dust and of other crushed and milled materials like cement follows a probability curve with a similar pattern as well-known physical functions such as the Maxwdl-BoUzmann distribution (Section 3.1.4) of the speed of gas molecules (Schubert and Waechtler, 1969). The so-called Rosin-Rammler-Sperling-Bennett (RRSB) function is given by ... 

Suggests that the root mean square (rms) speed of gas molecules is proportional to the square root of the gas temperature... 

Thermal neutrons are neutrons with a distribution of speeds nearly like the equilibrium distribution for gas molecules. In Chapter 9 the most probable speed of gas molecules of mass m is given as 2k TIm. Find the de Broglie wavelength of a neutron moving at the most probable speed for 300 K. Would thermal neutrons be useful for diffraction experiments to detamine crystal lattice spacings ... 

Isotopes of a different element have identical chemical properties. The only way to separate them is to find some physical process that is affected by the mass of the molecule. One of these is diffusion — the rate at which gases diffuse through a membrane of extremely small holes depends on their speed, which in turn depends on their mass. At the same temperature, the mean speed of gas molecules is inversely dependant on the square root of its mass. Thus a molecule four times as heavy would diffuse at half the rate. 

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