Thermo_ISM_ch16 - Chapter 16 Kinetic Theory of Gases...

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16-1 Chapter 16: Kinetic Theory of Gases Problem numbers in italics indicate that the solution is included in the Student’s Solutions Manual. Questions on Concepts Q16.1) Why is probability used to describe the velocity and speed of gas molecules? Velocity is a measure of kinetic energy. As with any large ensemble of particles (~N A ) not all of the particles will have the same energies. Instead, the particle energies are distributed through a range of values. The fraction of gas particles with a specific energy is defined by a probability. Q16.2) Describe pressure using gas kinetic theory. Why would one expect pressure to depend on the inverse of volume in this theory? Pressure arises due to collision of particles with the walls of the container. Since the pressure is dependent upon the number of particles striking the wall of the container per unit area, the pressure is dependent upon the density of the gas (number of particles per volume). As the volume increases, the density decreases, and the pressure will subsequently decrease. Q16.3) What are the inherent assumptions about gas particle interactions in gas kinetic theory? The assumptions made are that the particles do not interact at long distances (i.e., the intermolecular potential is zero when particles are separated) and) particles interact only through elastic collisions (total conservation of kinetic energy). Q16.4) Provide a physical explanation as to why the Maxwell speed distribution approaches zero at high speeds. Why is () 0 a t 0 f ν == ? Since kinetic energy content is related to temperature, higher particle speeds corresponds to a high inherent particle temperature. The ensemble of particles demonstrates an average temperature, and we can think of the inherent particle temperatures as distributed around this value. We would expect this number of particles demonstrating temperatures higher than the average temperature to decrease as the inherent temperature increases. Also, a non-zero distribution at infinite inherent temperature implies that the ensemble consists of an infinite number of particles. The distribution must reach zero as T 0 and T in order to preserve unit probability. Conversely, there can be no distribution at v = 0, due to the Uncertainty Principle since zero velocity would allow one to know both the position and velocity to arbitrary precision.
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Chapter 16/Kinetic Theory of Gases 16-2 Q16.5) How would the Maxwell speed distributions for He versus Kr compare if the gases were at the same temperature? The two distributions differ because of the mass difference between He and Kr. The Kr distribution will have a most probable speed that is smaller than He, the width of the Kr distribution will be smaller in comparison to He, and the Kr distribution will have a larger maximum amplitude.
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Thermo_ISM_ch16 - Chapter 16 Kinetic Theory of Gases...

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