The average coefficient of volume expansion for carbontetrachloride is 5.81x10^-
ID: 1680164 • Letter: T
Question
The average coefficient of volume expansion for carbontetrachloride is 5.81x10^-4. If a 50.0 gal steel container isfilled completely with carbon tetrachloride when the temperature is10.0 Celcius, how much will spill over when the temperature risesto 30.0 Celcius? The coefficient of expansion for steel is11x10^-6.I tried the solution that was posted for this chapter in mybook but I keep getting the wrong answer. The ans is 0.548gal
I tried the solution that was posted for this chapter in mybook but I keep getting the wrong answer. The ans is 0.548gal
Explanation / Answer
All right, I believe I have the answer to your question. I didn'tget the right answer on my first try, but using your given answer Imanaged to work out a method that I believe is correct. First, let's calculate the final volume of carbon tetrachloride.Its volume increases by a factor of 20*5.81*10^-4, so its finalvolume is 50 + 50*20*5.81*10^-4, or 50(1+20*5.81*10^-4). Now we need to calculate the final volume of the barrel. In thiscase, we can't directly calculate the volume of the barrel.Instead, we need to calculate the radial expansion andheight expansion. Suppose the initial radius is R. When the temperature is raised 20degrees, the radius will increase by a factor of 20*11*10^-6.Therefore, the final radius is R + R*20*11*10^-6, or R(1 +20*11*10^-6). If the initial height is H, the same goes. The final height is H(1+ 20*11*10^-6). Now the initial volume is simply R^2H. If we plug in our newvalues of R and H, we find that the new volume is: *[R(1+20*11*10^-6)]^2*H(1+20*11*10^-6) =R^2H*(1+20*11*10^-6)^3 The initial volume was 50, so R^2H = 50. Therefore, the finalvolume is: 50*(1+20*11*10^-6)^3 Now we simply subtract this from our final volume of the carbontetrachloride to find: Spill = 50(1+20*5.81*10^-4) - 50*(1+20*11*10^-6)^3 = .548 gal. Hope that helps!
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