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Unformatted text preview: aljabr (faa335) – Hw25 – Ross – (89251) 1 This printout should have 9 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. 001 10.0 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 nine gallons of gasoline are bought at 0 ◦ C rather than at 27 ◦ C (tempera ture at the filling station)? Correct answer: 0 . 630769 kg. Explanation: Given : ρ = 730 kg / m 3 , T = 0 ◦ C , T 1 = 27 ◦ C , β = 0 . 00096 ◦ C − 1 , 1 gallon = 0 . 0038 m 3 , and V = (9 gallons) parenleftbigg . 0038 m 3 gallon parenrightbigg = 0 . 0342 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 = (9 gallons) (0 . 00096 ◦ C − 1 ) (27 ◦ C) parenleftbigg . 0038 m 3 gallon parenrightbigg = 0 . 000886464 m 3 . The expanded specific volume of the gaso line is V = V + Δ V , which gives 1 ρ = 1 + β Δ T ρ , inverting ρ = ρ 1 + β Δ T , where ρ is the density of the gasoline at the higher temperature. Hence, the change in mass of gasoline for a constant defined gallon volume V (at 27 ◦ C rather than 0 ◦ C) is given by Δ m = ρ V ρV = ρ V parenleftbigg 1 1 1 + β Δ T parenrightbigg = ρ V β Δ T 1 + β Δ T = ρ Δ V 1 + β Δ T = ( 730 kg / m 3 ) ( . 000886464 m 3 ) 1 + (0 . 00096 ◦ C − 1 ) (27 ◦ C) = . 630769 kg . If you calculate the answer using the expres sion Δ m = ρ Δ V = ( 730 kg / m 3 ) ( . 000886464 m 3 ) = 0 . 647119 kg . you are wrong (close counts in horseshoes and handgrenades). The density, expansion coefficient, and conversion factor for gallons to m 3 is given at T = 0 ◦ C , not T = 27 ◦ C . 002 (part 1 of 2) 10.0 points At 8 ◦ C, an aluminum ring has an inner diam eter of 2 cm and a brass rod has a diameter of 2 . 07 cm....
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This note was uploaded on 01/27/2011 for the course PHYS 251 taught by Professor Gavrine during the Spring '10 term at Purdue.
 Spring '10
 Gavrine

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