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')

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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Question

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')

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