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{SECT 0 {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 0 "" {TEXT -1 34 
"Statistical Mechanics: Maxwell Gas" }}{PARA 19 "" 0 "" {TEXT -1 46 "b
y Darren Redfern, Tony Scott, Richard Pavelle" }}{PARA 257 "" 0 "" 
{TEXT 256 9 "Abstract:" }{TEXT -1 65 " Finds the most probable speed o
f a Maxwell-Botzman Distribution." }}{PARA 259 "" 0 "" {TEXT 259 28 "A
pplication Areas/Subjects: " }{TEXT 257 0 "" }{TEXT -1 69 " Science, E
ducation, Physics, Applied Math, Heat and Thermodynamics, " }}{PARA 
258 "" 0 "" {TEXT 258 9 "Keywords:" }{TEXT -1 83 "  education, Bohr, a
tom, Einstein, Maxwell-Boltzman, Statistical Mechanics, Maxwell" }}
{PARA 260 "" 0 "" {TEXT 260 9 "See Also:" }{TEXT -1 45 " MapleTech vol
 1 no 1, 1994 (& issue 7 1992)." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 12 " Maxwell Gas" }}
{PARA 0 "" 0 "" {TEXT -1 63 "Find the most probable speed of a Maxwell
-Botzman Distribution." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "n \+
:= v -> 4*Pi*(n.o)*((m/(2*Pi*k*T))^(3/2))*exp(-m*v^2/(2*k*T))*v^2:" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "n(v);" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 85 "The value v such that n(v) is maximized will be a po
int where the derivative is zero." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
19 "dv := diff(n(v),v):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "
CritPoints := solve(dv=0,v);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 81 "S
ince the speed v is by definition a magnitude, the negative result is \+
discarded." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "CritPoints := select(
t -> evalb(signum(op(1,t)) <> -1), [CritPoints]);" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 57 "Find the point of maximum via the second derivativ
e test." }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "for i from 1 to 2 do" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "    test.i := simplify(subs(v=CritP
oints[i],diff(n(v),v$2))):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "od;" }
}}{PARA 0 "" 0 "" {TEXT -1 92 "The point where the second derivative i
s negative is the point of maximum, the rms velocity." }}{PARA 0 "" 0 
"" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "if signum
(op(1,test1)) = -1 then maxv := CritPoints[1]" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 56 "elif signum(op(1,test2)) = -1 then maxv := CritPoints
[2]" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 3 "fi;" }}}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "8 0 0" 8 }{VIEWOPTS 1 1 0 1 1 1803 }