{VERSION 1 0 "X11/Motif" "1.0"}{GLOBALS 3 1}{FONT 0 "-adobe-helve
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lvetica-Bold" 12}{FONT 1 "-adobe-times-medium-r-normal--14-*" "ti
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Times-Bold" 8 14 64 "Times-Bold" 14}{SCP_R 1 0 17{COM_R 2 0{TEXT 
3 24 "Planck Radiation Formula"}}{COM_R 3 0{TEXT 1 0 ""}}{COM_R 4
 0{TEXT 1 74 "Statistical Mechanics\012by Tony Scott, Michael Mon
agan and Richard Pavelle.\015"}}{COM_R 5 0{TEXT 6 10 "Reference:"
}}{COM_R 6 0{TEXT 1 239 "D. McLaughlin, \"Symbolic Computation in
 Chemical Education\", Applications of Computer Algebra, Ed. by R
. Pavelle, Kluwer, Hingham, MA, (1985).\015\015T = temperature   
               \011k = Boltzmann's constant\011\011            h 
= Planck's constant\012\000"}}{COM_R 7 0{TEXT 1 49 "Telling Maple
 that these quantities are positive:"}}{INP_R 8 0 "> "{TEXT 0 38 
"assume(h>1): assume(k>1): assume(T>0):"}}{COM_R 9 0{TEXT 1 86 "\
015Getting the Stefan-Boltzmann Law     from the Planck Radiation
 Distribution function:"}}{INP_R 10 0 "> "{TEXT 0 44 "rho := v ->
 8*Pi*h*v^3/(exp(h*v/(k*T)) - 1);"}}{OUT_R 11 0 10{DAG :3n3\`rho`
@7,2n3\`v`,1,3n5\`operator`n4\`arrow`p7+3*9n3\`Pi`j2x0001n3\`h`p1
5a2x0001j2x0003+5(3n3\`exp`,2*9p17p15p1Ap15n3\`k`i2x0001n3\`T`p2A
p15p2Ap15p2Aj2x0008p7}}{INP_R 12 0 "> "{TEXT 0 65 "Energy:=Int(rh
o(nu),nu=0..infinity)= int(rho(nu),nu=0..infinity);"}}{OUT_R 13 0
 12{DAG :3n4\`Energy`=3(3n3\`Int`,3+3*9n3\`Pi`j2x0001n3\`h~~`pDn3
\`nu`j2x0003+5(3n3\`exp`,2*9pFpDp12pDn3\`k~~`i2x0001n3\`T~~`p22pD
p22pDp22j2x0008=3p12~3j2x0000n5\`infinity`+3*9pBj2x0005pFi2x0003p
20j2x0004p24p3F/3p2Bj2x0015}}{COM_R 14 0{TEXT 1 133 "This is the 
Stefan-Boltzmann Law (of Blackbody radiation).  The energy is pro
portional to T^4 and the constant of proportionality is:"}}{INP_R
 15 0 "> "{TEXT 0 26 "sigma:=coeff(op(2,\"),T,4);"}}{OUT_R 16 0 
15{DAG :3n4\`sigma`+3*7n3\`Pi`j2x0005n3\`h~~`i2x0003n3\`k~~`j2x00
04/3j2x0008j2x0015}}{COM_R 17 0{TEXT 1 35 "This is known as Stefa
n's constant."}}{INP_R 18 0 "> "{TEXT 0 0 ""}}}{END}
