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Homework Help: Immersion heater probelm

  1. Mar 30, 2006 #1
    Extracted from another thread tha had got a bit messy.

    The immersion heater in an electric hot water system is rated at 9 kW. If the tank is initially filled with 40 gallons (about 150 litres, with a mass of 150 kg) of cold water at 15 oC, how long will it take the heater to raise the temperature to 40 oC?

    Ok this is as far as I have got:

    Q=CmdeltaT

    deltaT=40-15 = 25

    q=Q=4196*150*25

    15735000J

    Ok so now I need to get time.

    p=deltaq/deltat

    So to get time do I just say time=p*delta q ???
     
  2. jcsd
  3. Mar 30, 2006 #2

    Hootenanny

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    Almost but not quite, i think you algerbraic skills are letting you down;

    [tex]P = \frac{\Delta Q}{\Delta t} [/tex]

    [tex]P\Delta t = \Delta Q[/tex]

    [tex]\Delta t = \frac{\Delta Q}{P}[/tex]

    Your theory is right, just the manipulation. A quick check to see if your manipulation is right is to take a look at the units.

    -Hoot:smile:
     
  4. Mar 30, 2006 #3
    So I need to do the calcualtions for each of these steps?

    Yes I am having problems with solving for variables it just seems so complicated. Do you know of any good tutorials for this?
     
  5. Mar 30, 2006 #4

    Hootenanny

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    No, all you have done is re-arranged an equation, you can just plug your numbers in for P and [itex]\Delta Q[/itex](which you have calculated earlier).

    I'm afraid I don't, but a quick internet search would probably show up a few. If you can get hold of a high school mathematics textbook, that would probably be best.

    -Hoot:smile:
     
  6. Apr 3, 2006 #5
    So this the solution????

    The immersion heater in an electric hot water system is rated at 9 kW. If the tank is initially filled with 40 gallons (about 150 litres, with a mass of 150 kg) of cold water at 15 oC, how long will it take the heater to raise the temperature to 40 oC?

    Q=CmdeltaT

    deltaT=40-15 = 25

    Q=4196*150*25

    15735000J

    delta t= delta q/p

    1748.33 =15735000/9000

    1748 seconds
     
  7. Apr 3, 2006 #6

    Hootenanny

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    Yep, that looks right to me

    -Hoot:smile:
     
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