How to calculate power required to heat water?

Discussion in 'Science' started by Fat80y, Feb 24, 2009.

  1. Fat80y

    Fat80y Member

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    Hey all,

    I'm in the planning stage of building a parts washer. What I need to do is calculate the size of the heating element I need to reach the temperatures required.

    Eg 200l water @ 45 degrees will need xxxx watt heating element to reach 90 degrees in 30 minutes.

    OR

    200l of water @ 45 degrees and 2000w heating element will take xxx minutes to heat to 90 degrees.

    Assume insulated container if that will affect things...
     
  2. amano.ginji

    amano.ginji Member

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    Yay, physics!

    Specific heat of water is 4.186 joules/gram degree C

    So to heat up 200L of water, we need:

    Q = cm(dT), where c is the specific heat, m is the mass, and dT is the change in temperature in Kelvin (Always better to work in Kelvin for thermodynamics), and Q is how much energy we need to do that.

    Q = 4.186 J/g K *200,000g * 45K = 37,674,000 joules required to heat 200L of water from 45 deg to 90 deg

    1 Watt is 1 joule/second, and hence:

    37,674,000 J / (30*60)seconds = 20 930 watts, so you'd need a 21kW element to do it, given perfect conditions, i.e., the element converts electricity to heat perfectly (it won't), nothing is lost though the tank (it is, the tank is heated as well, and the air outside the tank, and if there's a breeze blowing past it, that cools it further...)

    This is a bit more realistic given that 240V @ 10A gives 2400W of power.

    So we know the energy requirement (37,674,000 J), so at 2000W:

    37,674,000 J/2000(J/s) = 5.23 hours.

    At 2400W = 4.36 hours

    At 3600W (15A line, possible) = 2.9 hours.
     
  3. Eddyah

    Eddyah Member

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    ^ Looks good except you assumed the water was at 0 degrees celcius :Pirate:
     
  4. Oosh

    Oosh Member

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    Except all we care about is the delta.
     
  5. amano.ginji

    amano.ginji Member

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    dT = (T2 - T1) = (90 - 45)= 45 ;)
     
  6. Eddyah

    Eddyah Member

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    Ahh i'm a silly goose. I thought he wanted to heat a body of water to 45 degrees :cool:
     
  7. spludgey

    spludgey Member

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    This isn't completely right as C is not constant, but it's definitely close enough to answer the question.
    I was actually going to dig out the old steam tables, but this works too. :thumbup:
     
  8. OP
    OP
    Fat80y

    Fat80y Member

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    Thanks amano, a very informative reply :thumbup::thumbup::thumbup:
     
  9. amano.ginji

    amano.ginji Member

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    Yea, it does change - but I'd be willing to be that loss due to the environment and inefficiencies in the heating element would have a larger effect on the answer. Also, without a stiring mechanism in the water heater, depending on the number of elements, the water will heat unevenly, meaning you get hotter water around the element and cooler further way - and you'll get a longer heating time as a result.

    NP, got to use this physics degree I'm studying for something :)
     

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