Question

Suppose you use an average of 460 kW·h of electric energy per month in your home. (a) How long would 1.00 g of mass converted to electric energy with an efficiency of 38.0 % last you? (b) How many homes could be supplied at the 460 kW·h per month rate for one year by the energy from the described mass conversion?

Answer 1

Consider the following relationship.

Eneegy E = mc²

where m is mass and c is speed of light

E=10^-3(310⁸ )²

E=910¹³ J

The efficency is 38%

Hence energed used is

E=910¹³0.38

E= 3.42 10¹³ J

Energy required by houshold in one month = 460 Kw H

                                                            = 46010003600 J =1656000000 J

Energy required by houshold in one Year=121656000000

= 1.987 10¹⁰ J

so

Reqired Tme (in year)=(3.42 10¹³)/(1.987 10¹⁰)

                               =1721 Years

(b)

For this again (3.4210¹³)/(1.98610¹⁰) =1721 homes