# Homework Help: Temp. rise that will cause liquid to fill vessel completely

1. Dec 15, 2016

### King_Silver

• 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. Dec 15, 2016