# hw25b - aljabr(faa335 – Hw25 – Ross –(89251 1 This...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: aljabr (faa335) – Hw25 – Ross – (89251) 1 This print-out should have 9 questions. Multiple-choice 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 horse-shoes and hand-grenades). 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....
View Full Document

## This note was uploaded on 01/27/2011 for the course PHYS 251 taught by Professor Gavrine during the Spring '10 term at Purdue.

### Page1 / 4

hw25b - aljabr(faa335 – Hw25 – Ross –(89251 1 This...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online