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Nov. 05, 2001 Dr. Larry Dennis, FSU Department of Physics1 Physics 2053C – Fall 2001 Chapter 13 Temperature & Ideal Gases

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2 CAPA 7 & 8 A scuba tank has a volume of 3900 cm 3. For very deep dives, the tank is filled with 50% (by volume) pure oxygen and 50% pure helium. 7. How many oxygen molecules are there in the tank if it is filled at 20°C to a gauge pressure of 12.5 atm? PV = NkT N = PV/(kT) N = (13.5 * 1.013 x 10 5 N/m 2 *.00195 m 3 ) ( 1.38 x 10 -23 J/K * 293 K) N = 6.60 x 10 23

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3 CAPA 7 & 8 A scuba tank has a volume of 3900 cm 3. For very deep dives, the tank is filled with 50% (by volume) pure oxygen and 50% pure helium. 8. How many helium molecules are there in the tank if it is filled at 20°C to a gauge pressure of 12.5 atm? PV = NkT The same number as there are oxygen molecules. N = 6.60 x 10 23

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4 Kinetic Theory of Gasses 1. Gases contain a large number of molecules moving in random directions with a variety of speeds. 2. Molecules are very far apart and don’t exert forces on one another except when they collide. 3. Molecules obey Newton’s Laws. 4. Collisions are perfectly elastic.

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5 Kinetic Theory of Gasses The kinetic energy of the gas is directly related to it’s temperature. KE = ½ m(v 2 ) ave = 3/2 kT Only depends on temperature. V rms = (V 2 ) ave ( root mean square velocity ) V rms = (3kT)/m

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6 RMS Velocity T = 100 K T = 200 K T = 300 K v f V rms = (3kT)/m KE total = 3/2 NkT KE one = 3/2 kT Gas molecules have a distribution of speeds. The range of speeds depends on the temperature.

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7 CAPA 9 & 10 A scuba tank has a volume of 3900 cm 3. For very deep dives, the tank is filled with 50% (by volume) pure oxygen and 50% pure helium. 9. What is the ratio of the average kinetic energies of the two types of molecules? KE = 3/2 kT (for each molecule) Since the gases are at the same temperatures they have the same kinetic energies. Ratio = 1.0

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8 CAPA 9 & 10 A scuba tank has a volume of 3900 cm 3. For very deep dives, the tank is filled with 50% (by volume) pure oxygen and 50% pure helium. 10. What is the ratio of the rms speeds of the two types of molecules? V rms = (3KT/m) V rms (He)/V rms (O 2 ) = ( m(O 2 )/m(He) ) V rms (He)/V rms (O 2 ) = ( 2*16/(4) ) V rms (He)/V rms (O 2 ) = 8 = 2.83

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9 Quiz #8 Temperature Scales Fahrenheit Centigrade Kelvin Ideal Gas Law PV = nRT or PV = NkT Gauge Pressure Pay careful attention to units.

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10 Quiz #8 Kinetic Theory of Gasses Motion of molecules, Temperature KE = 3/2 kT (average kinetic energy of a molecule). KE = 3/2 nRT (kinetic energy of a mol of molecules. Avogadro’s Number (6.02 x 10 23 molecules/mol) V rms = (3kT/m) ½ average speed of a molecule.

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11 Quiz #8 Questions, Chap. 13: 21 Problems, Chap. 13: 5, 28, 35, 47, 88

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12 Problem 28 What are the following temperatures on the Kelvin scale? (K = C + 273.15 ) 1. 86 °C K = 86 + 273 = 359 K 2. 78 °F C = 5/9(F-32) C = 5/9*(78-32) =25.5 K = 299 K 3. -100 °C K = -100 + 273 K = 173 °C 4. 5500 °C K = 5500 + 273 K = 5773 °C

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13 Problem 88 What is the rms speed of nitrogen molecules contained in a 7.6 m 3 volume at 4.2 atm if the total amount of nitrogen is 1800 mols. V rms = (3kT)/m m(N 2 ) = 4.7 x 10 -26 kg Find T from PV = nRT T = PV/(nR) T = 4.2 atm * 7600 L 0.0821 (L-atm)*1800 mol/(mol K) T = 216 K

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14 Problem 88 What is the rms speed of nitrogen molecules contained in a 7.6 m 3 volume at 4.2 atm if the total amount of nitrogen is 1800 mols. V rms = (3kT)/m m(N 2 ) = 4.7 x 10 -26 kg V rms = [(3*1.38 x 10 -23 J/K * 216 K)/4.7 x 10 -26 kg ] ½ V rms = 436 m/s T = 216 K

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15 Next Time Quiz #8. Begin Chapter 14 – Heat. Please see me with any questions or comments. See you on Wednesday.

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