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(a) A neutron of mass
and kinetic energy K makes a head-on elastic collision with a stationary atom of mass m. Show that the fractional kinetic energy loss of the neutron is given by
for each of the following acting as the stationary atom: (b) hydrogen, (c) deuterium, (d) carbon, and (e) lead. (f ) If K = 1.00 MeV initially, how many such head-on collisions would it take to reduce the neutron’s kinetic energy to a thermal value (0.025 eV) if the stationary atoms it collides with are deuterium, a commonly used moderator? (In actual moderators, most collisions are not head-on.)
A control scheme is to be developed for the evaporator shown in Fig. metioned. The feed and product streams are mixtures of a solute and a solvent, while the vapor stream is pure solvent. The liquid level is tightly controlled by manipulating the feed flow rate, . The product composition, , and the feed flow rate, , are to be controlled by manipulating the product flow, , and the steam flow rate, . The evaporator "economy" is approximately constant, because of solvent are evaporated for each of steam. The flow rates have units of , while the compositions are expressed in weight fraction of solute. Derive an expression for the relative gain array for this system.