Temp. rise that will cause liquid to fill vessel completely

In summary, the conversation is about a problem with a question regarding a closed spherical storage tank of 30m^3 filled to 99% capacity with Nitric acid. The tank is made of stainless steel and the goal is to determine the temperature at which the liquid will completely fill the tank. The thermal expansion coefficients for the steel and acid are given as alpha = 12x10^-6 and beta = 8x10^-4, respectively. The equation set up to solve the problem is 0.99V(1+beta*delta T)=V(1+3alpha*delta T), with the desired answer being 13.26 degrees Celsius. Despite trying different approaches, the answer keeps resulting in an incorrect value
  • #1
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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  • #2
Stepwise, please.
 

FAQ: Temp. rise that will cause liquid to fill vessel completely

1. What is the relationship between temperature and liquid filling a vessel?

The relationship between temperature and liquid filling a vessel is that as temperature increases, the volume of the liquid also increases, causing it to eventually fill the vessel completely.

2. What happens to the molecules of a liquid as temperature increases?

As temperature increases, the molecules of a liquid gain energy and move faster, causing them to take up more space and expand the volume of the liquid.

3. Can temperature rise cause a liquid to overflow a vessel?

Yes, if the temperature continues to rise, the volume of the liquid will continue to increase until it surpasses the capacity of the vessel and overflows.

4. Is there a specific temperature at which a liquid will completely fill a vessel?

The specific temperature at which a liquid will completely fill a vessel depends on the type of liquid and the size and shape of the vessel. However, as temperature increases, the likelihood of the liquid filling the vessel also increases.

5. Can other factors besides temperature affect the volume of a liquid in a vessel?

Yes, the volume of a liquid in a vessel can also be affected by factors such as pressure, the type of material the vessel is made of, and the presence of any impurities in the liquid.

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