P3C.9 At low temperatures there are two contributions to the heat capacity of a metal, one associated with lattice vibrations, which is well-approximated by the Debye T-law, and one due to the valence electrons. The latter is linear in the temperature. Overall, the heat capacity can be written (a) Assuming that the expression given above for the heat capacity applies, explain why a plot of C,m(T)/T against T² is expected to be a straight line with slope a and intercept b. (b) Use such a plot to determine the values of the constants a and b. (c) Derive an expression for the molar entropy at temperature T. (Hint: you will need to integrate Cm(T)/T.) (d) Hence determine the molar entropy of potassium at 2.0 K. Debye electronic Cp.m (T)= aT³ + bT The molar heat capacity of potassium metal has been measured at very low temperatures to give the following data T/K 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.437 0.560 0.693 0.838 0.996 1.170 1.361 1.572 (JK' mol')

P3C.9 At low temperatures there are two contributions to the heat capacity of a metal, one associated with lattice vibrations, which is well-approximated by the Debye T-law, and one due to the valence electrons. The latter is linear in the temperature. Overall, the heat capacity can be written (a) Assuming that the expression given above for the heat capacity applies, explain why a plot of C,m(T)/T against T² is expected to be a straight line with slope a and intercept b. (b) Use such a plot to determine the values of the constants a and b. (c) Derive an expression for the molar entropy at temperature T. (Hint: you will need to integrate Cm(T)/T.) (d) Hence determine the molar entropy of potassium at 2.0 K. Debye electronic Cp.m (T)= aT³ + bT The molar heat capacity of potassium metal has been measured at very low temperatures to give the following data T/K 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.437 0.560 0.693 0.838 0.996 1.170 1.361 1.572 (JK' mol')

Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter2: The First Law Of Thermodynamics

Section: Chapter Questions

Problem 2.56E: What are the numerical values of the heat capacities c-v and c-p of a monatomic ideal gas,in units...

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