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3 August, 18:22

A recent home energy bill indicates that a household used 475475 kWh (kilowatt‑hour) of electrical energy and 135135 therms for gas heating and cooking in a period of 1 month. Given that 1.00 therm is equal to 29.329.3 kWh, how many milligrams of mass would need to be converted directly to energy each month to meet the energy needs for the home?

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  1. 3 August, 18:49
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    Given that,.

    A house hold power consumption is

    475 KWh

    Gas used is

    135 thermal gas for month

    Given that, 1 thermal = 29.3 KWh

    Then,

    135 thermal = 135 * 29.3 = 3955.5 KWh

    So, total power used is

    P = 475 + 3955.5

    P = 4430.5 KWh

    Since 1 hr = 3600 seconds

    So, the energy consumed for 1hr is

    1KW = 1000W

    P = energy / time

    Energy = Power * time

    E = 4430.5 KWhr * 1000W / KW * 3600s / hr

    E = 1.595 * 10^10 J

    So, using Albert Einstein relativity equation

    E = mc²

    m = E / c²

    c is speed of light = 3 * 10^8 m/s

    m = 1.595 * 10^10 / (3 * 10^8) ²

    m = 1.77 * 10^-7 kg

    Then,

    1 kg = 10^6 mg

    m = 1.77 * 10^-7 kg * 10^6 mg / kg

    m = 0.177mg

    m ≈ 0.18 mg
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