ism_chapter_17 - 1313 Chapter 17 Temperature and the...

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Unformatted text preview: 1313 Chapter 17 Temperature and the Kinetic Theory of Gases Conceptual Problems *1 • ( a ) False. If two objects are in thermal equilibrium with a third, then they are in thermal equilibrium with each other. ( b ) False. The Fahrenheit and Celsius temperature scales differ in the number of intervals between the ice-point temperature and the steam-point temperature. ( c ) True. ( d ) False. The result one obtains for the temperature of a given system is thermometer- dependent. 2 • Determine the Concept Put each in thermal equilibrium with a third body; e.g., a thermometer. If each body is in thermal equilibrium with the third, then they are in thermal equilibrium with each other. 3 • Picture the Problem We can decide which room was colder by converting 20 ° F to the equivalent Celsius temperature. Using the Fahrenheit-Celsius conversion, convert 20 ° F to the equivalent Celsius temperature: ( ) ( ) C 67 . 6 32 20 32 9 5 F 9 5 C ° − = ° − ° = ° − = t t so colder. was room s Mert' 4 •• Picture the Problem We can apply the ideal-gas law to the two vessels to decide which of these statements is correct. Apply the ideal-gas law to the particles in vessel 1: 1 1 1 1 kT N V P = Apply the ideal-gas law to the particles in vessel 2: 2 2 2 2 kT N V P = Divide the equation for vessel 1 by the equation for vessel 2: 2 2 1 1 2 2 1 1 kT N kT N V P V P = Chapter 17 1314 Because the vessels are identical and are at the same temperature and pressure: 2 1 1 N N = and 2 1 N N = ( ) correct. is a 5 •• Determine the Concept From the ideal-gas law, we have . V T nR P = In the process depicted, both the temperature and the volume increase, but the temperature increases faster than does the volume. Hence, the pressure increases. *6 •• Determine the Concept From the ideal-gas law, we have . P T nR V = In the process depicted, both the temperature and the pressure increase, but the pressure increases faster than does the temperature. Hence, the volume decreases. 7 • True. The kinetic energy of translation K for n moles of gas is directly proportional to the absolute temperature T of the gas ( ) nkT K 2 3 = . 8 • Determine the Concept We can use M RT v 3 rms = to relate the temperature of a gas to the rms speed of its molecules. Express the dependence of the rms speed of the molecules of a gas on their absolute temperature: M RT v 3 rms = where R is the gas constant, M is the molar mass, and T is the absolute temperature. molecules. the of speed rms the double to order in quadrupled be must re temperatu the , Because rms T v ∝ 9 • Picture the Problem The average kinetic energy of a molecule, as a function of the temperature, is given by kT K 2 3 av = and the pressure, volume, and temperature of an ideal gas are related according to . NkT PV = Express the average kinetic energy of a molecule in terms of its temperature: kT K 2 3 av = Temperature and the Kinetic Theory of Gases 1315 From the ideal-gas law we have: NkT PV = Eliminate kT between these...
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ism_chapter_17 - 1313 Chapter 17 Temperature and the...

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