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24 January, 16:22

A small immersion heater is rated at 255 W. The specific heat of water is 4186 J/kg⋅C°.

Estimate how long it will take to heat a cup of soup (assume this is 250 ml of water) from 17 °C to 62 °C. Ignore the heat loss to the surrounding environment.

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  1. 24 January, 17:05
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    0.2093 s

    Explanation:

    First, we the energy needed to heat the cup of soup

    Q = cm (t₂-t₁) ... Equation 1

    Where c = specific heat capacity of water, m = mass of water, t₂ = Final temperature, t₁ = initial temperature.

    Given: c = 4186 J/kg.°C, m = density of water*volume of water,

    Where density of water = 1 kg/m³, volume of water = 250/1000000 = 0.00025 m³,

    Therefore, m = 1*0.00025 = 0.00025 kg, t₂ = 62°C, t₁ = 17 °C

    Substitute into equation 1

    Q = 4186 (0.00025) (62-17)

    Q = 47.0925 J.

    Secondly we look for the time using

    W = Q/t ... Equation 2

    Where W = power rating of the heater.

    make t the subject of the equation

    t = Q/W ... Equation 3

    Given: W = 225 W

    Substitute into equation 4

    t = 47.0925/225

    t = 0.2093 s
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