Question

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

Answer 1

Answer:

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

Given:

Power of a single bulb = 100 W

Time period, T = 1 yr = $365\times 24\times 60\times 60$ = 31,536,000 s

mass of matter, m = 1 g = $1\times 10^{-3}]$

Solution:

According to Eintein's mass-energy equivalence:

E = $mc^{2}$

E = $1\times 10^{-3}\times (3\times 10^{8})^{2}$

E =  $9\times 10^{13} J$

Power of a single bulb, P =  $\frac{E}{T}$

                                       P =  $\frac{9\times 10^{13} }{31,536,000}$

                                       P = 28,53,881 W

No. of 100 W bulbs, n = $\frac{P}{power of one bulb}$

                                 n = $\frac{28,53,881}{100}$

                                 n = 28,539