Question

An imaginary country's annual (yearly) electric energy consumption was reported to be roughly 236 billion kWh. If we could generate this energy from pure mass to energy conversion, how much mass do we need in units of grams? Express your answer using ZERO decimal place. Please take the speed of light c=3.00 x 10⁸ m/s.

Answer 1

Energy generated from mass to energy conversion is given by:

E = M*c^2

c = speed of light = 3*10^8 m/sec

M = mass required = ?

E = energy required for whole country = 236 billion kW-h

Since we know that

1 kWh = 3.6*10^6 J

So,

Energy required = 236 billion kWh = 236*10^9 kWh = 236*10^9*3.6*10^6 J

So required amount of mass will be

m = E/c^2

m = (236*10^9*3.6*10^6)/(3*10^8)^2

m = 9.44 kg

Required mass in grams will be

m = 9440 grams

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