Molecular speeds, distribution

Figure 1-7 A Molecular Speed Distribution. The probability density is the expected number of speeds within an infinitesimal speed interval dv.

The points represent a typical result of a molecular speed distribution measurement. They are superimposed on the theoretical curve. To obtain the fraction of molecules with speeds in the range from v to v + Av, multiply f(v) by Av. 

A typical result of a molecular speed distribution measurement. 

Figure 5.18 (a) Apparatus for studying molecular speed distribution at a certain temperature. The vacuum pump causes the molecules to travel from left to right as shown, p) The spread of the deposit on the detector gives the range of moiecuiar speeds, and the density of the deposit is proportional to the number of molecules moving at different speeds. 

An analogy for molecular speed distributions features a common toy, the Frisbee. Reggie L. Hudson, "Toy Flying Saucers and Molecular Speeds," y. Chem. Educ., Vol. 59, 1982, 1025-1026. 

Boltzmann made many other significant contributions to science, particularly in the area oi statistical mechanics, which is the derivation of bulk thermodynamic properties for large collections of atoms or molecules by using the laws of probability. For example, the molecular speed distributions shown in Figure 10.19 are derived by using statistical mechanics such plots are known as Maxu eU—Boltzmann distributions. 

FIGURE 3.4 An asymmetric function with the same functional dependence as the Maxwell-Boltzmann molecular speed distribution. With this simple function, we can see that the maximum is exactly at 1 and the overall distribution is asymmetric to the high values. 

Maxwell derived the equation in 1860, but it took until 1955 for direct experimental verification of this equation to be made. The experimental determination of the molecular speed distribution is described on page 221. 

This function describes the molecular speeds distribution of the ideal gas. The resultant curve is presented in Figure 3.9 together with the constituent functions. 

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