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Chapter 21 The Kinetic Theory of Gases

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Quick Quiz 21.1 Two containers hold an ideal gas at the same temperature and pressure. Both containers hold the same type of gas but container B has twice the volume of container A. The average translational kinetic energy per molecule in container B is (a) twice that for container A (b) the same as that for container A (c) half that for container A (d) impossible to determine

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Answer: (b). The average translational kinetic energy per molecule is a function only of temperature. Quick Quiz 21.1

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Quick Quiz 21.2 Two containers hold an ideal gas at the same temperature and pressure. Both containers hold the same type of gas but container B has twice the volume of container A. The internal energy of the gas in container B is (a) twice that for container A (b) the same as that for container A (c) half that for container A (d) impossible to determine

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Answer: (a). Because there are twice as many molecules and the temperature of both containers is the same, the total energy in B is twice that in A. Quick Quiz 21.2

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Quick Quiz 21.3 Two containers hold an ideal gas at the same temperature and pressure. Both containers hold the same type of gas but container B has twice the volume of container A. The rms speed of the gas molecules in container B is (a) twice that for container A (b) the same as that for container A (c) half that for container A (d) impossible to determine

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Answer: (b). Because both containers hold the same type of gas, the rms speed is a function only of temperature. Quick Quiz 21.3

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Quick Quiz 21.4 How does the internal energy of an ideal gas change as it follows path i -> f in the figure below? (a) There is not enough information to determine how E int changes. (b) E int increases. (c) E int decreases. (d) E int stays the same.

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Answer: (b). According to Equation 21.10, E int is a function of temperature only. Because the temperature increases, the internal energy increases. Quick Quiz 21.4

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Quick Quiz 21.5 How does the internal energy of a gas change as it follows path f -> f along the isotherm labeled T + ΔT in the figure in question 4 above? (a) E int increases. (b) E int decreases. (c) E int stays the same. (d) There is not enough information to determine how E int changes.

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Answer: (c). Along an isotherm, T is constant by definition. Therefore, the internal energy of the gas does not change. Quick Quiz 21.5

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Quick Quiz 21.6 The molar specific heat of a diatomic gas is measured at constant volume and found to be 29.1 J/mol · K. The types of energy that are contributing to the molar specific heat are (a) translation only (b) translation and rotation only (c) translation and vibration only (d) translation, rotation, and vibration

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Answer: (d). The value of 29.1 J/mol · K is 7R/2. According to Figure 21.7, this suggests that all three types of motion are occurring. Quick Quiz 21.6

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Quick Quiz 21.7 The molar specific heat of a gas is measured at constant volume and found to be 11R/2. The gas is most likely to be (a) monatomic (b) diatomic (c) polyatomic

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Answer: (c). The highest possible value of C V for a diatomic gas is 7R/2, so the gas must be polyatomic. Quick Quiz 21.7

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Quick Quiz 21.8 Consider the qualitative shapes of the two curves in the figure below, without regard for the numerical values or labels in the graph. Suppose you have two containers of gas at the same temperature. Container A has 10 5 nitrogen molecules and container B has 10 5 hydrogen molecules. The correct qualitative matching between the containers and the two curves in this figure is (a) container A corresponds to the blue curve and container B to the brown curve (b) container B corresponds to the blue curve and container A to the brown curve (c) both containers correspond to the same curve.

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Answer: (a). Because the hydrogen atoms are lighter than the nitrogen molecules, they move with a higher average speed and the distribution curve is stretched out more along the horizontal axis. See Equation for a mathematical statement of the dependence of N v on m. Quick Quiz 21.8

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