# Energy Balance of Isothermal Energy Storage Tank

1. May 29, 2014

1. The problem statement, all variables and given/known data
Using unsteady state energy balances, discuss why storing cold water will be better in a larger tank rather than a smaller one.

Assume the initial state where the tank is full.

3. The attempt at a solution
I've tried to make this an algebraic exercise where I created arbitrary conditions where:

$V_{1}=2V_{2}$

which I would try and convert using properties from first principle values (density, mass, heat capacities) to get a situation where:

$\frac{dT}{dt}= Cf(t)$

where C is a coefficient which is carried down from the initial condition that $V_{1}=2V_{2}$, I would substitute $V_{1} and 2V_{2}$ into the equation and comparing the C values to prove that the change in temperature over time will be less in $V_{1}$ by a factor of C. And thus, proving that a larger volume will be able to sustain temperatures for a greater amount of time.

This is all my thinking however, I just wanted to know if my outlined approach was even possible to begin with.