- #1
miniradman
- 196
- 0
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:
[itex]V_{1}=2V_{2}[/itex]
which I would try and convert using properties from first principle values (density, mass, heat capacities) to get a situation where:
[itex]\frac{dT}{dt}= Cf(t)[/itex]
where C is a coefficient which is carried down from the initial condition that [itex]V_{1}=2V_{2}[/itex], I would substitute [itex]V_{1} and 2V_{2}[/itex] into the equation and comparing the C values to prove that the change in temperature over time will be less in [itex]V_{1}[/itex] 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.