B.5) I think we are to read the plots of Figure T5.2 finding the x=kT/e for which the y-axis (essentially speciic heat) is 1/2 its high temperature value. We then convert x to T using the value of e: T=e x/k 1-d oscillator x=.3 1d motion x=.8 diatomic rotation x=.4 a: * ? 1e-7*.8/kb .9283650331310271E-03 b: * ? .00025*.4/kb 1.160456291413784 c: * ? .29*.3/kb 1009.596973529992 M.3) * ? hbar*3e14/kb 2291.470533294990 mostly switched off until thousands of K ----- z1=Sum[(2 j +1) Exp[-e b j(j+1)],{j,0,4}] avg1=-D[Log[z1], b] avg1=avg1 /. b->1/(k T) c1=D[avg1,T] c1 = c1 /. {e-> 87.6 k} c1=Simplify[c1/k] Plot[c1,{T,10,100}] Export["H2_c1.eps",%] Howework Questions: Explain what/why of the following bit of code: avg1=-D[Log[z1], b] the average energy is (-) the beta derivative of the log of the partition function c1=D[avg1,T] the specific heat is how the energy changes with temperature Plot[c1,{T,1,10}] fails: "too small to represent as a normalized machine number" Plot[c1,{T,100,1000}] shows a falling specific heat due to termination of the infinite sum at high temperatures the occupation of states equalizes and there is no change with temeprature z2=Sum[(2 j +1) Exp[-e b j(j+1)],{j,0,8}] avg2=-D[Log[z2], b] avg2=avg2 /. b->1/(k T) c2=D[avg2,T] c2 = c2 /. {e-> 87.6 k} c2=Simplify[c2/k] Plot[c2,{T,100,250}] Export["H2_c2.eps",%] Plot[{c1,c2},{T,80,200}] Export["H2_c1+c2.eps",%] Plot[c2,{T,250,1000}] also shows a declining specific heat (but its not that much of a decline) z3=Integrate[Exp[-e b u],{u,0,Infinity},Assumptions->{e b >0}] avg3=-D[Log[z3], b] avg3=avg3 /. b->1/(k T) c3=D[avg3,T] c3 = c3 /. {e-> 87.6 k} In[28]:= c3=Simplify[c3/k] Out[28]= 1 allc[T_]:=If[T<100,c1, If[T<300,c2,c3]] Plot[allc[T],{T,10,200},PlotRange->All] Export["H2_allc.eps",%]