Final answer:
To calculate the energy density of U-235 for nuclear fuel, the mass change from fission is converted into energy using E=mc² and the known conversion factors, resulting in an estimated energy density given in terrajoules per kilogram.
Step-by-step explanation:
To estimate the energy density of nuclear fuels, specifically uranium-235 (U-235), we begin by understanding that during nuclear fission, a small amount of mass is converted into energy according to Einstein's mass-energy equivalence principle, E=mc2. Based on the provided example of 17 million kcal/g per fission event and known mass-to-energy conversions, we can conduct a calculation to find the energy density.
Step-by-Step Calculation:
- Calculate the mass change in kg from a.m.u. using the given conversion (1 a.m.u. = 1.6605 x 10-27 kg).
- Apply E=mc2 to convert mass change to energy in joules.
- Convert energy from joules to kilocalories.
- Finally, scale up to terrajoules by dividing by 4,184 J/kcal and adjusting units accordingly to give energy density in terrajoules per kilogram.
It is important to note that the energy per kilogram of fission fuel is less than that of fusion fuel due to fewer moles per kilogram of the heavy nuclides, although each individual fission reaction yields more energy than a fusion reaction.