Question

If 3.6 g of a substance is completely converted into energy, then the electrical energy derived from it will be.
1. 9 × 10¹⁰ kWH
2. 9 × 10⁷ kWH
3. 3.24 × 10¹⁰ kWH
4. 3.24 × 10⁷ kWH

Answer 1

Correct Answer - Option 2 : 9 × 10⁷ kWH

Concept:

The energy equivalence of mass is given by equation

E = m c ²

m is mass, c is speed of light

c = 3 × 10 ⁸ m /s

Kilowatt Hour: It is unit of energy consumed by an electrical device having power 1 kilowatt in duration of 1 hour.

1 KwH = 3.6 × 10 ⁶ Joule

Calculation:

Given, mass m = 3.6 gm = 3.6 × 10 ^-3 kg

c =  3 × 10 8 m /s

Energy

E = (3.6 × 10 -3 kg ) (3 × 10 8 m /s ) ²  Joule

If we divide this by 3.6 × 10 6 Joule we will get result in KwH

\(E = \frac{3.6 × 10^{-3} × 3 × 10^8 × 3 × 10^8}{3.6 × 10^6} KwH\)

⇒ E = 9 × 10 ^{(-3 + 8 + 8 - 6)} KwH = 9 × 10 ⁷ KwH

So, the correct option is 9 × 107 kWH