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where Eqs. (7.3-10) and (7.3-11) were used. Equation (7.3-17) has the usual units for discharge loss of watts per beam-amp or electron-volts per ion. As expected, maximizing the current and voltage efficiencies minimizes the discharge loss. As an example of discharge loss in a Hall thruster, consider the SPT-100 thruster operating at the nominal 1.35-kW discharge power and 300 V. The discharge current is then 1350/300 = 4.5 A. The thruster is reported [4-61 to have values of 771, = 0.7 and q, = 0.95. The cost of producing beam ions is then

Chlorination of Alkanes Free-radical chlorination is the most commonly used method for the chlorination of a saturated hydrocarbon I,106-108,111,112 Both thermal and photochemical processes may be carried out in the liquid or vapor phase The liquid-phase photochemical procedure is preferred for polychlorination; gas-phase photochemical reactions can yield either mono- or polychlorinated product Chlorine atoms are highly energetic and reactive species, bringing about extremely long kinetic chain length in free-radical chlorination Both propagation steps are fairly facile, and reversal of hydrogen abstraction is negligible Hydrogen abstraction by a chlorine atom from any alkane is exothermic Since the transition state in exothermic chlorination resembles the reactants more than the products, resonance stabilization does not play a significant role in the reaction On the basis of their extensive studies, Hass, McBee, and coworkers formulated some simple general rules of free-radical chlorination.

8. Computation gives:

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l13 For example, no carbon skeleton rearrangements occur during chlorination if catalysts and excessively high temperatures are avoided The relative reactivity of substitution of hydrogens is tertiary> secondary> primary This is due to the strongly electrophilic character of the chlorine atom reacting more readily with hydrogen bonded to a tertiary carbon of higher electron density Activation energies, however, are very similar, and reactivity differences further diminish with increasing temperature The relative reactivity ratio of 44: 33 : 1 at 300 C, for example, approaches 1: 1 : 1 with increasing temperature l13 Because of the high dissociation energy of the C-H bond, methane is quite unreactive toward radical attacks compared with other alkanes 114 As a result, free-radical chlorination of alkanes is a nonselective process Except when only one type of replaceable hydrogen is present (methane, ethane, neopentane, unsubstituted cycloalkanes), all possible monochlorinated isomers are usually formed.

Instead of the heat balance approach as described above, Equation 2.2 can be derived directly from Equation 2.3 by replacement of the derivatives with the respective nite difference approximations. The nite difference approximation for the time derivative is as shown in Equation 2.4. The second order derivative in the x-dimension can be approximated as follows: T T Ti +1 - Ti Ti - Ti -1 T - 2Ti + Ti -1 2 T T x + x Dx Dx = = i +1 2 x x Dx Dx x Dx 2 Note that in the nite difference approximation for the second order derivative as shown above, the temperature gradients are evaluated from the temperature difference between node i and each of the adjacent nodes at the two sides of node i. This scheme is, therefore, called a central-in-space difference scheme. Since Equation 2.2 relates the change in the temperature at node i to the temperatures at the nodes at both sides of node i, it applies only to the interior nodes within a slab of material. Boundary conditions The nite difference equation for the outermost slice of a slab of material can also be derived from the heat balance approach. Using Te to denote the sol-air temperature or environmental temperature of the surrounding, the convective and radiant heat ux at the surface can be described by: qo = ho (Te - Ts ) (2.6)

Although alkyl chlorides are somewhat less reactive than alkanes, di- and polychlorinations always occur The presence of a chlorine atom on a carbon atom tends to hinder further substitution at that carbon The one exception is ethane that yields more 1, l-dichloroethane than 1,2-dichloroethane The reason for this is that chlorination of an alkyl chloride occurs extremely slowly on the carbon atom adjacent to the one bearing the chlorine atom (vicinal effect)115 During slow thermal chlorination, elimination of HCI from the monochloride with the resultant formation of an alkene followed by chlorine addition may be the dominant route to yield dichloroalkanes This mechanism, however, is negligible in rapid thermal or photochemical reactions Substantially increased selectivity of monochlorination were observed in certain solvents 114,1 16-1 18 This is explained as a result of the interaction of the electrophilic (ie.

Start No Indirect seawater cooled Yes TC3 = TSW Air cooled Yes TC1 = TAmb TC1 = TSW No From known qE, calculate WC, qC, TC2 & RG: WC = WC (qE, TC1) (chiller model) ; qC = qE + WC ;

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