Question

If the energy in fusion bombs were used to supply the energy needs of the world, how many of the 9-megaton variety would be needed for a year’s supply of energy (using data from Table 7.1)? This is not as farfetched as it may sound—there are thousands of nuclear bombs, and their energy can be trapped in underground explosions and converted to electricity, as natural geothermal energy is.

Short answer

Number of 9-megaton fusion bomb required for a year’s supply of energy is $10526$.

Step-by-step solution

Definition of Concepts

Conservation of energy:An isolated system's total energy is always conserved. In other words, the energy neither be not created nor be destroyed; it can be only transformed from one form to another.

Number of 9-megaton fusion bomb required for a year’s supply of energy

The energy released by 9-megaton fusion bomb can be trapped in underground explosions and converted to electrical energy.

The energy release of 9-megaton fusion bomb is,

$E_{bomb}=3.8\times {10}^{16}\text{J}$

Annual consumption of energy in the world is,

$E_{consumption}=4\times {10}^{20}\text{J}$

Therefore, the number of 9-megaton fusion bomb required to fulfil the demand is,

$n=\frac{E_{consumption}}{E_{bomb}}$

Putting all known values,

$$\begin{gathered} n=\frac{4\times {10}^{20}\text{J}}{3.8\times {10}^{16}} \\ \approx 10526 \end{gathered}$$

Therefore, $10526$9-megaton fusion bomb required for fulfilling the annual consumption of energy for a year.