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hw 1 oscar_pdf - maldonado(om2892 Homework 1 2010...

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maldonado (om2892) – Homework 1 2010 – Stone – (13750) 1 This print-out should have 24 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 2) 5.0 points A copper rod and a steel rod are heated. At 0 C the copper rod has a length of L C , the steel one has a length of L S . When the rods are being heated or cooled, a difference of 7 . 25 cm is maintained between their lengths. Find the value of L C . Correct answer: 13 . 2917 cm. Explanation: Given : d = 7 . 25 cm , α C = 1 . 7 × 10 5 ( C) 1 , and α S = 1 . 1 × 10 5 ( C) 1 . For d = L S - L C = 7 . 25 cm to be constant, the rods must expand by equal amounts: α C L C Δ T = α S L S Δ T L s = α C L C α S or d = α C L C α S - L C α S d = α C L C - α S L C Hence L C = α S d α C - α S = bracketleftbig 1 . 1 × 10 5 ( C) 1 bracketrightbig (7 . 25 cm) 1 . 7 × 10 5 ( C) 1 - 1 . 1 × 10 5 ( C) 1 = 13 . 2917 cm . 002 (part 2 of 2) 5.0 points Find the value of L S . Correct answer: 20 . 5417 cm. Explanation: L s = L c + d = 13 . 2917 cm + 7 . 25 cm = 20 . 5417 cm . 003 (part 1 of 3) 3.0 points Consider neon, a noble gas whose molecules consist of single atoms of atomic mass 0 . 02 kg / mol. Avogadro’s number is 6 . 02 × 10 23 mol 1 , and Boltzmann’s constant is 1 . 38 × 10 23 J / K. What is the average kinetic energy of a neon atom when the gas is at a temperature of 480 K? Correct answer: 9 . 936 × 10 21 J. Explanation: Let : T = 480 K and k = 1 . 38 × 10 23 J / K . The average kinetic energy of a gas molecule, one neon atom in this case, is 1 2 m v 2 av = 3 2 k T = 3 2 (1 . 38 × 10 23 J / K) (480 K) = 9 . 936 × 10 21 J . 004 (part 2 of 3) 3.0 points What is the root-mean-square speed of a neon atom under such conditions? Correct answer: 773 . 4 m / s. Explanation: Let : M = 0 . 02 kg / mol and N A = 6 . 02 × 10 23 mol 1 . The mass of one neon atom is m = M N A = 0 . 02 kg / mol 6 . 02 × 10 23 mol 1 = 3 . 32226 × 10 26 kg
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maldonado (om2892) – Homework 1 2010 – Stone – (13750) 2 so the root-mean-square speed is v rms = radicalbig v 2 av = radicalbigg m v 2 av m = radicalbigg 3 k T m = radicalBigg 3 (1 . 38 × 10 23 J / K) (480 K) 3 . 32226 × 10 26 kg = 773 . 4 m / s . 005 (part 3 of 3) 4.0 points The internal energy of a monoatomic ideal gas such as neon is simply the total kinetic energy of all its atoms. What is the internal energy of 9 liters of neon at a temperature of 480 K and pressure of 0 . 89 atm? Correct answer: 1216 . 18 J. Explanation: Let : P = 0 . 89 atm = 90157 Pa and V = 9 L = 0 . 009 m 3 . At temperature 480 K and pressure 0 . 89 atm, the number of moles of 9 liters of neon is n = P V R T So, the internal energy is E = ( n N A ) parenleftbigg 1 2 m v 2 av parenrightbigg = P V N A R T parenleftbigg 3 2 k T parenrightbigg = 3 2 P V = 3 2 (90157 Pa) (0 . 009 m 3 ) = 1216 . 18 J . 006 10.0 points One liter of water at 49 C is used to make iced tea. How much ice at 0 C must be added to lower the temperature of the tea to 19 C? The specific heat of water is 1 cal / g · C and latent heat of ice is 79 . 7 cal / g.
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