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Temp. rise that will cause liquid to fill vessel completely

  1. Dec 15, 2016 #1
    • Moved from a technical forum, so homework template missing
    I've a problem with a question regarding a closed spherical storage tank of 30m^3.
    Its filled to the 99% mark with Nitric acid and the tank is made of stainless steel.
    I'm trying to determine the temperature rise that will cause the liquid to completely fill the vessel.

    I know that as the temperature increases, both the steel and the liquid will expand and I am given the thermal expansion coefficients as follows:

    alpha (steel) = 12x10^-6
    beta (acid) = 8x10^-4

    I currently have the equation set up as follows:

    0.99V (1+ beta *delta T) = V (1 + 3 alpha *delta T)

    The answer is supposed to be 13.26 degrees C.

    however I keep ending up with something stupid looking like "0.997884" which is entirely wrong!

    I've tried doing this as well:
    0.99 + 0.99 (8x10^4 T) = 1 + 36x10^-6 T

    however again! that is giving me 0.001584 T = 1.000036 T

    what on earth am I doing wrong/right?
     
  2. jcsd
  3. Dec 15, 2016 #2

    Bystander

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    Stepwise, please.
     
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