It is a common observation that matter and energy are closely related. For example, a mass of water flowing into the turbines of a hydro-electric plant leads to the generation of electricity; the rearrangement of hydrogen, oxygen, and carbon in chemical compounds in an internal combustion engine generates power to move a car; a neutron-induced splitting of a heavy nucleus produces heat to generate steam; two light nuclei may fuse and immediately break up with the reaction products possessing considerable kinetic energy. Each of these examples illustrates a transformation from one state of matter and energy to another in which an attendant release of energy has occurred.

These matter-energy transformations may be represented in various forms. For the hydro-electric process we may write

m(hi)-^m(h2) (1-1)

where m(hi) and m(h2) is a mass of water at an initial elevation hi and final elevation h2; the resultant energy E released can be evaluated by computing (mghi — mgh2), where g is the local acceleration due to gravity.

An example of an exothermic chemical reaction is suggested by the process

CH4 +202 -*2H20+C02 (1.2)

*

with an energy release of about 5 eV.

The case of neutron induced fission of a 235U nucleus is represented by

n+235t/->vn + £p; (1.3)

І

where n is a neutron, Pj is a particular reaction product, and n is the number of neutrons emitted in this particular process. Here, the total energy released possesses a slight dependence on the kinetic energy of the initiating neutron but

Appendix A provides equivalents of various physical quantities.

3

is typically close to 200 MeV.

The fusion reaction likely to be harnessed first is given by

2 H+2H —» n+4He (1.4)

with an energy release of 17.6 MeV. Accounting for the fact that the above species react as nuclei, we assign in a more compact notation the names deuteron, triton, and alpha to the reactants and reaction product, to give

d +1 —» n + a. (1.5)

The fundamental features of matter and energy transformation are thus evident. In the hydroelectric case, a mass of water has to be raised to a higher level of potential energy-performed by nature’s water cycle-and it subsequently attains a lower state with the difference in potential energy appearing as kinetic energy available to generate electricity. For the case of chemical combustion, an initial energetic state of the molecules corresponding to the ignition temperature of the fuel, has to be attained in order to induce a chemical reaction yielding thereupon new chemical compounds. The energy release thereby is due to the more tightly bound reaction product compounds with a slightly reduced total mass; such a mass defect is generally manifested in energy release-typically in the eV range for chemical reactions. In the case of fission, the initiating neutron needs to possess some finite kinetic energy in order to stimulate the rearrangement of nuclear structure; interestingly, the thermal motion of a neutron at room temperature is sufficient for the case involving nuclei such as 235U. For fusion to occur, the reacting nuclei must possess sufficient kinetic energy to overcome the electrostatic repulsion associated with their positive charges before nuclear fusion can take place; the alternative of fusion reactions at low temperature is also possible and will be discussed later. Again, in the case of fission and fusion, the reaction products emerge as more tightly bound nuclei and hence the corresponding mass defect determines the quantity of nuclear energy release-typically in the MeV range.

Evidently then, a more complete statement of the above processes is therefore provided by writing an expression containing both matter and energy terms in the form

Ein “t* A7 m ^ Eout 47 out (1-6)

with the masses measured in energy units, i. e. multiplied by the square of the speed of light. The corresponding process is suggested graphically in Fig. 1.1.

The depiction of Fig. 1.1 suggests some useful generalizations. Evidently, a measure of the effectiveness and potential viability for energy generation by such transformations involves microscopic and macroscopic details of matter-energy states before and after the process. In addition, it is also necessary to include considerations of the relative supply of the fuel, Mi„, the toxicity of reaction products, Mout, the magnitude of Eou, relative to Ein, as well as other technological, economic and ecological considerations. Additional issues may include availability of the required technology, deployment schedules, energy conversion losses, management and handling of the fuel and of its reaction products,