Question

A recent home energy bill indicates that a household used 345 kWh 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?

Answer 1

0.2775 mg

Step-by-step explanation:

Electrical Energy = 345 kWh

Converting to joules

1 kWh = 1000×3600 J

345×1000×3600 = 1242×10⁶ J

Energy used for gas = 225 therm

1 therm = 29.3 kWh

So,

225 therm = 225 × 29.3 = 6592.5 kWh = 6592.5×1000×3600

Total energy = 345×1000×3600+6592.5×1000×3600 = 6937.5×1000×3600

Mass–energy equivalence

E=mc²

`m=(E)/(c^2)\\\Rightarrow m=(6937.5* 1000* 3600)/(9* 10^16)=0.0000002775\ kg`

∴ Mass that would need to be converted directly to energy each month to meet the energy needs for the home is 0.2775 mg