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Math Help - Work out how long it takes to warm up water

  1. #1
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    Work out how long it takes to warm up water

    Hello,

    I'm trying so very hard to work out how long it will take to warm up 5 liters of water.

    500 watt heating element
    Battery = 12V power, 40 Amps

    Amount of water = 5 liters
    Final Temp = 65 degrees
    Ambient Temp = 45 degrees

    Ive worked out that it takes 41.86 K joules to heat the required water, so how do i then work out how long it will take to heat up using the specified equipment?

    Thanks in advanced!

    Rob
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  2. #2
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    Quote Originally Posted by robert jr View Post
    500 watt heating element
    Battery = 12V power, 40 Amps

    Amount of water = 5 liters
    Final Temp = 65 degrees
    Ambient Temp = 45 degrees

    Ive worked out that it takes 41.86 K joules to heat the required water, so how do i then work out how long it will take to heat up using the specified equipment?
    1 watt is 1 joule per second. The heating element is rated at 500 watts, but the battery can only deliver 1240 = 480 watts, so I assume that that is all that is available for heating. If the figure of 41.86 kJ is correct then the time taken for the heating element to deliver this amount of energy will be \frac{41.86\times10^3}{480} seconds. (That's a bit less than one and a half minutes, which sounds a bit fast to heat up that amount of water. But we are assuming that no energy is lost, and that the entire 480 watts goes into heating the water.)
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  3. #3
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    thanks! yeh it seems a little to quick, it turns out that it actually takes 1750082.4 J to heat the water. so it would take 59 mins??

    im confused
    Last edited by robert jr; October 22nd 2008 at 12:41 PM.
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  4. #4
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    I believe that if you heat 1 gramme of water by 1 degree celsius you will use 4.2 joules. So to heat 5 litres = 5000 grammes through 20 should take about 5000204.2 = 420,000 joules.
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  5. #5
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    thanks,

    i understand now
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