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Energy Balance of Isothermal Energy Storage Tank

  1. May 29, 2014 #1
    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:

    [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.
     
  2. jcsd
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