(a) What is the Dulong-Petit Law? Under what eireumstances is it accurate? 2 (b) Einstein's thermal model begins wi...
(a) What is the Dulong-Petit Law? Under what eireumstances is it accurate? 2 (b) Einstein's thermal model begins with the assumption that the average energy for 1 mole of oscillators is given by the expression, Show that this leads to the following expression for the heat capacity Cmol, E/T hwg where E mol (eesT-1) 141 (c) Using the last expression given in part (b) for Cmol, show for the two extremes of the temperature range, (i) In the low temperature limit where T « ΘΕ that Cmal 3R (9). e-et. (ii) In the high temperature limit where T-oothat Cmol 3R [4] Hint: LHopital's Rule says that if we have an indeterminate limit of the form 0/0 or oo/oo, then (d) Paying careful attention to the two expressions just derived in parts (cXi) and (cXii) above, sketch the behaviour of Cmol as a function of temperature T, making 12] sure to label the axes. (e) What do the two limits in part (c) say about the successes and failures of the Einstein thermal model? 12)
(a) What is the Dulong-Petit Law? Under what eireumstances is it accurate? 2 (b) Einstein's thermal model begins with the assumption that the average energy for 1 mole of oscillators is given by the expression, Show that this leads to the following expression for the heat capacity Cmol, E/T hwg where E mol (eesT-1) 141 (c) Using the last expression given in part (b) for Cmol, show for the two extremes of the temperature range, (i) In the low temperature limit where T « ΘΕ that Cmal 3R (9). e-et. (ii) In the high temperature limit where T-oothat Cmol 3R [4] Hint: LHopital's Rule says that if we have an indeterminate limit of the form 0/0 or oo/oo, then (d) Paying careful attention to the two expressions just derived in parts (cXi) and (cXii) above, sketch the behaviour of Cmol as a function of temperature T, making 12] sure to label the axes. (e) What do the two limits in part (c) say about the successes and failures of the Einstein thermal model? 12)