Energy Balance of Isothermal Energy Storage Tank

[miniradman]

Homework Statement

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.

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.

 

[KataKoniK]

Your approach seems reasonable and could be a good way to demonstrate why storing cold water in a larger tank would be more beneficial. However, keep in mind that energy balances can also take into account other factors such as heat transfer rates, so you may want to consider incorporating those into your analysis as well. Additionally, you may want to discuss the concept of thermal inertia and how a larger volume of water has a greater thermal inertia, meaning it takes longer for its temperature to change. This could also contribute to why storing cold water in a larger tank would be better. Overall, your approach is a good starting point but be sure to consider other factors and explain the concept of thermal inertia in your analysis.