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How much time require to heat?

  1. Aug 23, 2012 #1
    1. The problem statement, all variables and given/known data

    A Heating Element rated 1400Watt Supply 220V
    Current : 6.36 Amperes
    Resistance = 34.57 Ohms

    Area to be heated L X B X H = 4inches X 4inches X 9inches

    From Temperature 35 Deg.C to 1000 Deg.C

    All under standard/normal pressure
    2. Relevant Question
    How long would it take to heat from 35 Deg.C to 1000 Deg.C

    3. The attempt at a solution

    Joules = Mass(Kg) X Heat Capacity on kJ/Kg.DegC X Delta T

    Inch(s) -> to Meter(s)
    4 -> 0.1016
    4 -> 0.1016
    9 -> 0.2286


    Therefore Volume of Air = 0.00235974 Mt^3

    Density of Air @ 35. Deg C = 1.1455 Kg/Mt^3

    Amount of Air @ 35. Deg C = 0.00235974 X 1.1455 = 0.0027031 Kg

    Heat Capacity of Air = 1.06 kJ/kg Deg.C

    Delta T = 1000 - 35 = 965 Deg.C

    Joules to be consumed = 0.0027031 x 1.06 X 965 = 2.76499 kJ = 2764.99 Joules

    Joules = Current^2 X resistance X time(Seconds)

    Then 27466.99 = (6.36)^2 X 34.57 X T(Seconds)
    or, T = 1.97 Seconds (Something is wrong)


    Time=? (to raise the temperature from 35 Deg.C to 1000 Deg.C)

    3. The attempt at a solution
     
    Last edited: Aug 23, 2012
  2. jcsd
  3. Aug 23, 2012 #2
    Did you use Cp instead of Cv?
     
  4. Aug 23, 2012 #3
    your 'joules to be consumed'.... 2764.99 does not match the Joules (27466.99) on the next line.
    Is this a typing mistake you have made?
     
  5. Aug 26, 2012 #4
    Correct is 2764.99
    As 2.76499 kJ converted to Joules as 2764.99

    So help me how to find out the correct time as the time required cannot be 1.97secs
     
  6. Aug 26, 2012 #5
    What is constant? Pressure or volume?
     
  7. Aug 26, 2012 #6
    Your problem says nothing about a flow so one has to assume it is a fixed volume. Given that, you need constant volume specific heat rather than constant pressure specific which it seems you are using. The result will be less energy required so less time to heat.

    Are you sure you have the box dimensions correct. Placing a 1400 watt heater in a 4X4X9 inch box seems like overkill. This sounds like a toaster-oven to me which would take longer to heat because of the mass of the heating element and the ceramic core it is generally wound around.
     
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