Question

A recent home energy bill indicates that a household used 385 kWh (kilowatt-hour) of electrical energy and 125 therms for gas heating and cooking in a period of 1 month. Given that 1.00 therm is equal to 29.3 kWh, how many milligrams of mass would need to be converted directly to energy each month to meet the energy needs for the home? Answer in mg.

Answer 1

So we have to convert all given energy in to mass.

So we can apply E=mc².

We have to convert all energy in joule as follows

385 kWh x 3600 sec/hr * 1000 W/kW = 1.39 x 10⁹ J
125 therm x 29.3 kWh x 3600 x 1000 = 1.32 x 10¹⁰ J

Total energy = 1.46 x 10¹⁰ J

E = m x c²
1.46 x 10¹⁰ J = m x (3.0 x 10⁸)²

m = 1.6 x 10^-7 kg

So m = 0.16 mg