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SM_chapter21 - 21 The Kinetic Theory of Gases CHAPTER...

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21 The Kinetic Theory of Gases 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 Distribution of Molecular Speeds 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 The alcohol evaporates, absorbing energy from the skin to lower the skin temperature. *Q21.4 (i) Statements a, d, and e are correct statements that describe the temperature increase of a gas. (ii) Statement b is true if the molecules have any size at all, but molecular collisions with other molecules have nothing to do with temperature. (iii) Statement c is incorrect. The molecular collisions are perfectly elastic. Temperature is determined by how fast molecules are moving through space, not by anything going on inside a molecule. *Q21.5 (i) b. The volume of the balloon will decrease. (ii) c. The pressure inside the balloon is nearly equal to the constant exterior atmospheric pressure. Snap the mouth of the balloon over an absolute pressure gauge to demonstrate this fact. Then from PV nRT = , volume must decrease in proportion to the absolute tempera- ture. Call the process isobaric contraction. *Q21.6 At 200 K, 1 2 3 2 0 0 m k T B v rms0 2 = . At the higher temperature, 1 2 2 3 2 0 2 m k T B v rms0 ( ) = Then T T = = ( ) = 4 4 200 800 0 K K . Answer (d). *Q21.7 Answer c > a > b > e > d. The average vector velocity is zero in a sample macroscopically at rest. As adjacent equations in the text note, the asymmetric distribution of molecular speeds makes the average speed greater than the most probable speed, and the rms speed greater still. The most probable speed is (2 RT M ) 1 2 and the speed of sound is ( γ RT M ) 1 2 , necessarily smaller. Sound represents an organized disturbance superposed on the disorganized thermal motion of molecules, and moving at a lower speed. 543 13794_21_ch21_p543-570.indd 543 13794_21_ch21_p543-570.indd 543 12/27/06 12:04:44 PM 12/27/06 12:04:44 PM
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544 Chapter 21 *Q21.8 Answer (b). The two samples have the same temperature and molecular mass, and so the same rms molecular speed. These are all intrinsic quantities. The volume, number of moles, and sample mass are extrinsic quantities that vary independently, depending on the sample size.
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