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By Arthur Adamson (Auth.)

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1-66) works can be illustrated by the following example. Consider the gas molecules to be hard spheres so that the potential energy plot is as shown in Fig. 1-17. That is, there are no attractive forces, and (r) jumps to infinity at r = σ. The integral of Eq. (1-67) can then be written in two parts: (a) at r > σ, 4tr) = o, σ ,-

Describe two possible experimental situations for which this equation applies. 2 1 - 2 3 * Calculate Ρ versus V for N H using the van der Waals equation. D o this for 40°C 3 intervals between 0°C and 200°C and plot the results. Recast the data in terms of com­ pressibility factor Ζ in terms of P for various T and plot these curves. r r SPECIAL TOPICS PROBLEMS 37 1-24 Make a semiquantitative plot of (a) isobars for Ρ around P°\ and (b) isosteres for V around V/. Use the curves of Figs. 1-8 and 1-9 as a guide.

44 CHAPTER 2: KINETIC MOLECULAR THEORY OF GASES 2-3 The Distribution of Molecular Velocities We start by applying the Maxwell-Boltzmann distribution equation (2-7) to the case of a one-dimensional gas, that is, to a system of molecules having only kinetic energy due to motion along one direction in space, say the χ direction. The Boltzmann equation then gives 2 ( — -jyfY raW \ (2-21) where w is the 2velocity in the χ direction (and could be either positive or negative), and 6 = | raw . The more quantitative way of stating Eq.

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