Question

How many 100W light bulbs could be powered for one year by the direct conversion of 1g of matter into energy?

Answer 1

No. of 100 W bulbs, n = 28,539 bulbs

Given:

Power of a single bulb = 100 W

Time period, T = 1 yr =
`365* 24* 60* 60` = 31,536,000 s

mass of matter, m = 1 g =
`1* 10^(-3)]`

Solution:

According to Eintein's mass-energy equivalence:

E =
`mc^(2)`

E =
`1* 10^(-3)* (3* 10^(8))^(2)`

E =
`9* 10^(13) J`

Power of a single bulb, P =
`(E)/(T)`

P =
`(9* 10^(13) )/(31,536,000)`

P = 28,53,881 W

No. of 100 W bulbs, n =
`(P)/(power of one bulb)`

n =
`(28,53,881)/(100)`

n = 28,539