Temp. rise that will cause liquid to fill vessel completely

AI Thread Summary
A user is attempting to calculate the temperature rise needed to completely fill a closed spherical storage tank of 30m^3 filled with nitric acid, accounting for the thermal expansion of both the liquid and the stainless steel tank. They have the correct coefficients for thermal expansion but are struggling with their equations, yielding incorrect results. The established equation is 0.99V(1 + beta * delta T) = V(1 + 3 alpha * delta T), which should lead to a temperature rise of 13.26 degrees Celsius. Despite multiple attempts, the user is confused by their calculations, indicating a need for clearer step-by-step guidance. The discussion highlights the complexities of thermal expansion in closed systems.
King_Silver
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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?
 
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Stepwise, please.
 
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