Harvesting energy from hot, radioactive fuel from nuclear reactors I have a couple of questions about nuclear reactors used for electricity generation.
a) If the spent fuel is still radioactive and quite hot, why is it disposed off ? Why can't its energy be used / harvested to do any more work ?
b) Do all reactors use the radioactive fuel to heat a working fluid to propel a turbine ? Specifically, are there technologies / methods of directly harvesting the momentum of the fission particles and the radiation to do work ?
Thanks.
 A: a) To convert heat energy to electricity the heat energy has to be at sufficiently high temperature, as the latter limits the percentage of heat energy that can be converted to other energy forms. Very roughly the efficiency $\epsilon$ of an idealised heat machine is given by:
$$\epsilon\:\text{(%)} \approx 100 \times \big(1-\frac{T_H}{T_L}\big)$$
Where $T_H$ is the hottest point of the cycle and $T_L$ the coolest. Spent fuel just isn't hot enough and of course also dangerous to handle, further decreasing profitability.
b) Almost all civilian nuclear energy production relies on turning the fission energy into high temperature steam, used to drive turbines to generate electricity. Some minor specialist applications turn heat directly into small amounts of electrical energy.
A: In answer to your first question, the fuel in standard nuclear reactors is Uranium-235. The chain reaction that produces the heat is started by bombarding slow moving neutrons at U-235 nuclei - http://hyperphysics.phy-astr.gsu.edu/hbase/nucene/fission.html
The speed of these neutrons, and the choice of U-235 is very specific to the reaction. The spent fuel roads in a reactor have used most of the uranium content, leaving more stable fission products that can't be induced into a chain reaction - http://hyperphysics.phy-astr.gsu.edu/hbase/nucene/u235chn.html
The fuel rods coming out of the reactor may be hot because they've come out of a reactor with a temperature of a few hundred degrees, but theyre no longer contributing to maintaining that heat since they're not a part of the chain reaction anymore. They'll quickly lose this heat once they leave the reactor, so theyre not much use in terms of energy production.
Fuel rods coming out of a reactor can be very radioactive, as the fission products are usually unstable. These fuel rods are often called 'hot' by nuclear physicists, but that's in reference to the energy of the radiation released from them, not their temperature, and this radiation is hard to harness efficiently into energy.
In answer to your second question, the heat produced in the reactor is a measure of the increase in kinetic energy of the particles within the reactor, and the transfer of momentum from these particles to the coolant passing through it. So essentially the process is already directly harnessing the momentum of the particles.
