- That The Susteptibility 15 7 In The Intit B I V 3 Free Energy Of A Harmonic Oscillator A One Dimension Hamonic O 1 (49 KiB) Viewed 14 times
that the susteptibility 15 7 = in the intit B « I. v 3. free energy of a harmonic oscillator. A one-dimension: hamonic oscil- lator has an infinite series of equally spaced energy states, with 4 shes, where Problems Entropy 2 Figure 3.13 Entropy versus temperature for hardlonic Gillelor of frequency s is a positive inicger or zera, and is the classical frequency of the oscillator. We have chosen the zero of energy at the state s = 0. (a) Show it for it harmonic oscillator the free energy is fetlo [1 -- expl-fw/t]. 187) Note that at high temperatures such hatt >> hw we may expand the argument of the logarithum to obtain Fatlogie/t). (b) From (87) show that the entropy is (58) heeft explht) - 1 -log[t - expl - swt)]. The entropy is shown in Figure 3.13 and the heat capacity in Figure 1.14. 4. Energy fluctuations. Considera system of fixed volume in thermal contact with a reservoir show that the mean square fluctuation in the energy of the system is <le - - - U/Ct). Here is the conventional synibol for). Mint: Use the partition function 2 to relate U/Ct to the mean square ductuation. Also, multiply out the term Note: The temperature of a system is a quantity that by definition does (89)