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Current and resistance of wire heating up water

  1. Feb 1, 2017 #1
    1. The problem statement, all variables and given/known data
    An office worker uses an immersion heater to warm 250 g of water in a light, covered, insulated cup from 20 degrees C to 100 degrees C in 4 minutes. The heater is Nichrome resistance wire connected to 120V power supply. Assume wire is at 100 degree C during 4 minute time interval.

    a) calculate average power required to warm the water to 100 degree C in 4 min
    b) calculate the required resistance in the heating element at 100 degree C
    c) calculate the resistance of the heating element at 20 degree C
    d) derive a relationship between the diameter of the wire, resistivity at 20 degree C, rou (po), the resistance at 20 degree C, Ro, and the length L
    e) If L = 3 m, what is the diameter of the wire?

    What we are given:
    mass of water = 250 g
    density of water = 1000 kg / m^3
    change in T = 80
    V = 120V
    t = 4 minutes
    p of Nichrome = 150 *10^-8
    coeff of resistivity of Nichrome = 0.4 * 10^-3

    2. Relevant equations
    P = I*V = V^2/I = I^2*R
    R = V/I
    R = Ro [1 + coefficient of resistivity (T - To)]
    R = p L / A
    I = Q / t

    3. The attempt at a solution
    a) calculate average power required to warm the water to 100 degree C in 4 min
    density = m / v ... v = m / density
    v = A * L
    v = 250 / 1000 = .25 m ^3 = A * L
    R = p L / (.25/L) = p L^2 / .25

    How do I calculate I for Power without knowing the charge?
     
  2. jcsd
  3. Feb 1, 2017 #2

    gneill

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    Staff: Mentor

    You should know (or be able to look up) an expression that relates power to voltage and current. Of course, you'll need to have completed part (a) to find the power requirement first.
     
  4. Feb 3, 2017 #3

    rude man

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    Homework Helper
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    If the wire is at 100C then it can't heat the water in 4 minutes or any other finite amount of time ...
     
  5. Feb 3, 2017 #4

    CWatters

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    Science Advisor
    Homework Helper

    +1

    I suspect a badly designed question. I think they said to assume the wire is at a constant temperature so you would ignore it's thermal mass.
     
  6. Feb 3, 2017 #5

    rude man

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    Either that or the office worker wanted a long rest pause ... :smile:
     
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