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Edited on Fri Dec-07-07 07:22 AM by Lochloosa
1. The problem statement, all variables and given/known data
An underground gasoline tank at 54°F can hold 1100 gallons of gasoline. If the driver of a tanker truck fills the underground tank on a day when the temperature is 82°F, how many gallons, according to his measure on the truck, can he pour in? Assume that the temperature of the gasoline cools to 54°F on entering the tank.
2. Relevant equations
(delta)Length = 3(alpha) * Volume(initial) * (delta)Temp i found the value alpha for gasoline to be 9.6e-4
3. The attempt at a solution
3(9.6e-4)(28)(1100)=delta(L)=88.7 thus the amount he could pour in is 1188.7 for some reason this isn't the answer though... i'm not really sure what i'm doing wrong
The equation for volume expansion will look like this: \Delta V = \beta V_0 \Delta T
where \beta is the volume coefficient of expansion, which would be about 3 times the linear coefficient. Are you sure you found the linear coefficient of expansion for gasoline?
The 9.6e-4 already accounted for the times 3, and thus was the volume coefficient of expansion. I guess you couldn't really make one for gasoline anyway.
Solids
ΔL = L0 α ΔT linear ΔA = A0 2α ΔT superficial (areal) ΔL = L0 3α ΔT volumetric
Liquids
ΔV = V0βΔT
Liquids have higher expansivities than solids
β ≈ 10−3/K, 3α ≈ 10−5/K
Gases
behavior of gases is more complicated, gases will expand as much as pressure will allow
Coefficients of Thermal Expansion for Selected Materials material linear α (10−6 K−1) material volume β (10−6 K−1) aluminium 23.1 alcohol, ethyl 1120 barium ferrite 10 gasoline 950 brass 20.3 jet fuel, kerosene 990 carbon, diamond 1.18 mercury 181 carbon, graphite ∥ 6.5 water, liquid (1 °C) -50 carbon, graphite ⊥ 0.5 water, liquid (4 °C) 0 chromium 4.9 water, liquid (10 °C) 88 concrete 8 ~ 12 water, liquid (20 °C) 207 copper 16.5 water, liquid (30 °C) 303 germanium 6.1 water, liquid (40 °C) 385 glass 8.5 water, liquid (50 °C) 457 gold 14.2 water, liquid (60 °C) 522 iron 11.8 water, liquid (70 °C) 582 lead 28.9 water, liquid (80 °C) 640 nickel 13.3 water, liquid (90 °C) 695 platinum 8.8 plutonium 54 silicon 4.68 silver 18.9 solder, lead-tin 25 steel, stainless 17.3 steel, structural 12 tin 22 titanium 8.5 tungsten 4.5 uranium 13.9 water, ice (0 °C) 51 zinc 30.2
"What's more, the aircraft expands by 15-25 centimetres during flight because of the scorching heat created by friction with air. Designers used rollers to isolate the cabin from the body, so that stretching doesn't rip the plane apart." Helen Pearson "Concorde wings its way into retirement." Nature Physics Portal. October 2003. "Concorde measures 204ft in length - stretching between six and ten inches in-flight due to heating of the airframe. She is painted in a specially developed white paint to accommodate these changes and to dissipate the heat generated by supersonic flight."
invar water anomalous expansion of water ice is less dense than water water is most dense at 4 °C (ρ = 999.973 kg/m3) applications frozen pipes burst turnover of lake water in spring
:sarcasm:
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