Problem 25

  When 1.0 kg of coal is burned, about $3.0 \times 10^7$ J of energy is released. If the energy released per ²³⁵₉₂U fission is $2.0 \times 10^2$ MeV, how many kilograms of coal must be burned to produce the same energy as 1.0 kg of ²³⁵₉₂U?

SOLUTION: First, we want to determine the energy released by the uranium in Joules. To do that, note that 1 kg = 1000 g, there are 235 g/mol in uranium, there are $6.022 \times 10^{23}$ nuclei/mol by definition of mole, uranium releases 200 MeV per nuclei, and 931.5 MeV = $1.4924 \times 10^{-10}$ J, (whew!) so that the energy release by fission in Joules is

$$E = (1000 g) \left (\frac{1 mol}{235 g} \right ) \left (\fra... ...ht ) \left (\frac{1.4924 \times 10^{-10} J}{931.5 MeV} \right )$$

$$E = 8.2 \times 10^{13} J$$

Now, when 1 kg of coal is burned, $3 \times 10^7 J$ is released. So the amount of coal need to burn as much energy as 1 kg of uranium is

$$m_{coal} = (8.2 \times 10^{13})\left (\frac{1 kg}{3 \times 10^7 J} \right )$$

$$m_{coal} = 2.7 \times 10^6 kg$$