Thermo: Change in temp effect on volume of a steel container

AI Thread Summary
The discussion revolves around calculating the volume change of a steel container filled with carbon tetrachloride due to temperature increase. The average coefficient of volume expansion for carbon tetrachloride is given as 5.81 x 10^-4 (°C)^-1. The user initially attempted to apply the volume expansion formula but arrived at an incorrect result of 0.484 gallons, which was close to the correct answer. Ultimately, the user resolved the issue independently and expressed gratitude for any potential assistance. The conversation highlights the importance of correctly applying thermal expansion principles in practical scenarios.
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Homework Statement



The average coefficient of volume expansion for carbon tetrachloride is 5.81*10-4 (°C)-1. If a 49.0 gal steel container is filled completely with carbon tetrachloride when the temperature is 10.0°C, how much will spill over when the temperature rises to 27.0°C?

Homework Equations



ΔL = α*(original length)*ΔT


The Attempt at a Solution



I used this equation except instead of units of length, I substituted units of volume. So my final equation was:
ΔL = (5.81E-4 (°C)-1) * (49.0 gal) * (27°C - 10°C) = 0.484 gallons. This is incorrect, but within 10% of the correct answer. Not sure what I am doing wrong. Any help is greatly appreciated, Thank you!
 
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I have solved it - thanks anyway!
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
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Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
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