Question

A recent home energy bill indicates that a household used 425 kWh (kilowatt-hour) of electrical energy and 195 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

mass is 0.245 mg

Step-by-step explanation:

given data

power = 425 kWh = 1.53 ×
`10^(9)` J

gas heating = 195 therms = 195

time = 1 month

to find out

how many milligrams of mass need to meet energy needs for the home

solution

we know here that

1.00 therm = 29.3 kWh

so here 195 therms is equal to 195 ×29.3 × 3600 s

195 therms = 20.56 ×
`10^(9)` J

so total energy used

total energy = 1.53 ×
`10^(9)` + 20.56 ×
`10^(9)`

total energy = 22.09 ×
`10^(9)` J

and by einstein mass energy equation

E = mc² ..................1

m = E / c²

put here value

m = 22.09 ×
`10^(9)` / ( 3×
`10^(8)` )²

m = 2.45 ×
`10^(-7)` kg

so mass is 0.245 mg