81204hw14Sol

81204hw14Sol - Zzztayloe Rex – Homework 14 – Heinz –...

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Unformatted text preview: Zzztayloe, Rex – Homework 14 – Heinz – 81204 – Nov 04, 2004 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points Two thermometers are calibrated, one in de- grees Celsius and the other in degrees Fahren- heit. At what temperature are their readings nu- merically the same? Correct answer: 233 K. Explanation: The relation between the Fahrenheit tem- perature and the Celsius temperature is T C = 5 9 ( T F- 32) . If T C and T F have the same value T , then after solving T = 5 9 ( T- 32) 4 9 T =- 160 9 T =- 160 4 =- 40 ◦ C , Thus T K = T C + 273 =- 40 ◦ C + 273 = 233 K . 002 (part 1 of 1) 10 points A bridge is made with segments of concrete 74 m long (at the original temperature). If the linear expansion coefficient is 1 . 2 × 10- 5 ( ◦ C)- 1 , how much spacing is needed to allow for expansion for an increase in temperature of 49 ◦ F? Correct answer: 2 . 41733 cm. Explanation: Given : L = 74 m , α = 1 . 2 × 10- 5 ( ◦ C)- 1 , and Δ T F = 49 ◦ F . The temperature change is T C = 5 9 ( T F- 32 ◦ F) , Δ T C = 5 9 (Δ T F ) , and the length will expand by Δ L = αL Δ T = αL 5 9 Δ T F = £ 1 . 2 × 10- 5 ( ◦ C)- 1 / × (74 m) 5 9 (49 ◦ F) = 2 . 41733 cm . 003 (part 1 of 1) 10 points The density of gasoline is 730 kg / m 3 at 0 ◦ C. One gallon of gasoline occupies 0 . 0038 m 3 . Gasoline’s volume expansion coefficient is . 00096 ◦ C- 1 . How many extra kilograms of gasoline are obtained when eight gallons of gasoline are bought at 0 ◦ C rather than at 17 ◦ C (tempera- ture at the filling station)? Correct answer: 0 . 356358 kg. Explanation: Given : ρ = 730 kg / m 3 , T = 0 ◦ C , T 1 = 17 ◦ C , β = 0 . 00096 ◦ C- 1 , 1gallon = 0 . 0038 m 3 , and V = (8 gallons) µ . 0038 m 3 gallon ¶ = 0 . 0304 m 3 . The specific volume is V = 1 ρ , then Δ V = β V Δ T . The change in volume is Δ V = V β Δ T = (8 gallons)(0 . 00096 ◦ C- 1 ) (17 ◦ C) µ . 0038 m 3 gallon ¶ = 0 . 000496128 m 3 . Zzztayloe, Rex – Homework 14 – Heinz – 81204 – Nov 04, 2004 2 The expanded specific volume of the gaso-...
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81204hw14Sol - Zzztayloe Rex – Homework 14 – Heinz –...

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