Question

A recent home energy bill indicates that a household used 475 kWh (kilowatt-hour) of electrical energy and 225 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?(in mg)

Answer 1

Answering this question requires Einstein's mass-energy equivalance:

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Step 1) To find out how much mass needs to be converted ddirectly into energy to fuel the home for a month, the total energy needs of the house need to be determined. Start by finding the kilowatt-hour equivalent of the therms used, given that 225 therms were used, and that each therm is the same as 29.3 kWh:

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Step 2) Next, find the total energy used, given the 475 kWh of electricity used, and the 65.92 kWh equivalent of gas used:

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Step 3) Convert that to Joules:

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Step 4) Solve Einstein's equation for the mass m:

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Step 5) Fill in the 2.5443*10¹⁰ J that was found for the energy E, and 2.998*10⁸ m/s for the speed of light c:

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Step 6) Convert that to milligrams:

So 0.283 mg of matter would need to be converted directly into energy to fuel the home for the month.