Question

In nuclear fission and fusion reactions mass is converted into energy. The average person in US uses around 100,000,000 J of energy per year.
(a) Calculate the yearly energy consumption for a US population of 300 million.
(b) Using Einstein's famous formula, E = m c^2, calculate the energy that would be released if a 60 kg person were converted entirely into energy.
(c) How many years would this amount of energy support a population of 300 million?

Answer 1

Answer:

a) The yearly energy consumption for a US population of 300 million is $3\times 10^{16} J/year$

b) The energy that would be released if a 60 kg person were converted entirely into energy is $5.4\times 10^{18}$ Joules.

c) 180 years would this amount of energy support a population of 300 million.

Explanation:

a) Average energy consumed by single person of US = 100,000,000 J/year

Then 300 million US citizen will consume:

300 million = 300 × 1,000,000 = $3\times 10^8$

The yearly energy consumption for a US population :

$100,000,000 J/year\times 3\times 10^8=3\times 10^{16} J/year$

The yearly energy consumption for a US population of 300 million is $3\times 10^{16} J/year$

b) $E = m\times c^2$

E = Energy from converted mass of m

c = speed of light

Given mass of person = m = 60 kg

$E=60 kg\times (3\times 10^8 m/s)^2 = 5.4\times 10^{18} J$

c) Energy calculated in part (b) = $E=5.4\times 10^{18} J$

The yearly energy consumption for a US population  of 300 million in an year = $3\times 10^{16} J/year$

Let the that would be supported by $5.4\times 10^{18}$ Joules of energy be x.

$x\times 3\times 10^{16} J/year=5.4\times 10^{18} J$

$x=\frac{5.4\times 10^{18} J}{3\times 10^{16} J/year}=180 years$

180 years would this amount of energy support a population of 300 million.