Chapter 21

# Chapter 21 - 21 The Kinetic Theory of Gases CHAPTER OUTLINE...

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21 CHAPTER OUTLINE 21.1 Molecular Model of an Ideal Gas 21.2 Molar Specific Heat of an Ideal Gas 21.3 Adiabatic Processes for an Ideal Gas 21.4 The Equipartition of Energy 21.5 The Boltzmann Distribution Law 21.6 Distribution of Molecular Speeds 21.7 Mean Free Path The Kinetic Theory of Gases ANSWERS TO QUESTIONS Q21.1 The molecules of all different kinds collide with the walls of the container, so molecules of all different kinds exert partial pressures that contribute to the total pressure. The molecules can be so small that they collide with one another relatively rarely and each kind exerts partial pressure as if the other kinds of molecules were absent. If the molecules collide with one another often, the collisions exactly conserve momentum and so do not affect the net force on the walls. Q21.2 The helium must have the higher rms speed. According to Equation 21.4, the gas with the smaller mass per atom must have the higher average speed-squared and thus the higher rms speed. Q21.3 Yes. As soon as the gases are mixed, they come to thermal equilibrium. Equation 21.4 predicts that the lighter helium atoms will on average have a greater speed than the heavier nitrogen molecules. Collisions between the different kinds of molecules gives each kind the same average kinetic energy of translation. Q21.4 If the average velocity were non-zero, then the bulk sample of gas would be moving in the direction of the average velocity. In a closed tank, this motion would result in a pressure difference within the tank that could not be sustained. Q21.5 The alcohol evaporates, absorbing energy from the skin to lower the skin temperature. Q21.6 Partially evacuating the container is equivalent to letting the remaining gas expand. This means that the gas does work, making its internal energy and hence its temperature decrease. The liquid in the container will eventually reach thermal equilibrium with the low pressure gas. This effect of an expanding gas decreasing in temperature is a key process in your refrigerator or air conditioner. Q21.7 Since the volume is fixed, the density of the cooled gas cannot change, so the mean free path does not change. The collision frequency decreases since each molecule of the gas has a lower average speed. Q21.8 The mean free path decreases as the density of the gas increases. Q21.9 The volume of the balloon will decrease. The pressure inside the balloon is nearly equal to the constant exterior atmospheric pressure. Then from PV nRT = , volume must decrease in proportion to the absolute temperature. Call the process isobaric contraction. 601

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602 The Kinetic Theory of Gases Q21.10 The dry air is more dense. Since the air and the water vapor are at the same temperature, they have the same kinetic energy per molecule. For a controlled experiment, the humid and dry air are at the same pressure, so the number of molecules per unit volume must be the same for both. The water molecule has a smaller molecular mass (18.0 u) than any of the gases that make up the air, so the humid air must have the smaller mass per unit volume.
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