Example 9.2-1: Finding the Voltage required for a Given Temperature Rise in a Wire Heated by an Electrical Current
See worksheet p268.mws for a derivation of the equations used in this example. Start with equations 9.2-1 and 9.2-14 to get equation 9.2-17 > restart;I^2; Since Maple thinks I is sqrt(-1), we don't want to use I for the current > Se:=i^2/ke; eq 9.2-1 but using i for the current density instead of I. > dTmax:=Se*R^2/(4*k); eq 9.2-14 now leads to eq. 9.2-17 > i:=ke*E/L; eq. 9.2-18 > dTmax; giving eq. 9.2-19 > eq19:=dTmax=Tmax-T0; > s:=solve(eq19,E); > E:=s[1]; Giving us eq 9.2-20. Note the square brackets in s[1]. > R:=2*mm; L:=5*m;T0:=293*K; Tmax:=T0+10*K; Given data with units > k:=2.23e-8*volt^2*K^(-2)*ke*T0; Given the value for the Lorenz number of copper > E; Close to eq. 9.2-21 except: > mm:=m/1000; We need the relation between m and mm. > E; And we need to tell Maple that ke and volt are positive real variables. > assume(ke>0);assume(volt>0); > simplify(E); The text found 40 volts.
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