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?

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