Answer :
a) Energy that can be obtained from the U-235 in 1 kg of natural uranium is 8.06 × 10¹³ J.
The number of fissions per kilogram of U-235 is given as 1kg ÷ 235 g/mol ÷ Avogadro's number = 6.02 × 10²³ / 235 = 2.56 × 10²¹ fissions.
The total energy obtained is E = N × E_avg, where N is the number of fissions and E_avg is the average energy released per fission.
Therefore:
E = 2.56 × 10²¹ fissions × 198 MeV/fission × 1.6 × 10⁻¹³ J/MeV
E = 8.06 × 10¹³ J.
b) The energy content of coal varies depending on the type of coal, but assuming a typical value of 24 MJ/kg (megajoules per kilogram), the energy obtained from burning 1 kg of coal is 24 × 10⁶ J.
c) The Energy Information Administration estimates that the total coal resources in the United States amount to approximately 3.72 trillion short tons, or 3.37 × 10¹² kg.
At an average energy content of 24 MJ/kg, this corresponds to a total energy content of 8.09 × 10²² J.
The total U-235 resources are much smaller, estimated at around 70,000 tons.
Assuming an average energy release of 198 MeV/fission, the total energy content of these resources would be:
E = 70,000 tons × 2000 lbs/ton × 0.4536 kg/lb × 1 kg/235 g/mol ÷ Avogadro's number × 198 MeV/fission × 1.6 × 10⁻¹³ J/MeV = 4.52 × 10²¹ J.
Therefore, the total energy contained in US resources of coal and U-235 is approximately
8.09 × 10²² J + 4.52 × 10²¹ J = 8.54 × 10²² J.
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