Let's look at a copper crystal, where each copper atom donates one conduction electron to the crystal. a) Use the free electron model to determine the prediction for copper fermi energy EF, fermi temperature TF and degeneration pressure Pdeg (at temperature T = 0 K). b) Further calculate the contribution of the degeneration pressure to the isothermal compression coefficient of copper. B= -V др av T c) Finally, determine the model prediction for the electronic molar specific heat capacity Cv. The empirical form for this is Cy = yT and the experimentally determined value for copper is y = 0.695 mJ mol-¹ K-². Compare this numerical value with your result

Modern Physics
3rd Edition
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Chapter12: The Solid State
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Let's look at a copper crystal, where each copper atom donates one conduction electron to the
crystal.
a) Use the free electron model to determine the prediction for copper fermi energy EF, fermi
temperature TF and degeneration pressure Pdeg (at temperature T = 0 K).
b) Further calculate the contribution of the degeneration pressure to the isothermal
compression coefficient of copper.
B
=
-V
др
(SP)
T
c) Finally, determine the model prediction for the electronic molar specific heat capacity Cy .
The empirical form for this is Cy = yT and the experimentally determined value for copper is
Y = 0.695 mJ mol-¹ k-².
=
Compare this numerical value with your result
Transcribed Image Text:Let's look at a copper crystal, where each copper atom donates one conduction electron to the crystal. a) Use the free electron model to determine the prediction for copper fermi energy EF, fermi temperature TF and degeneration pressure Pdeg (at temperature T = 0 K). b) Further calculate the contribution of the degeneration pressure to the isothermal compression coefficient of copper. B = -V др (SP) T c) Finally, determine the model prediction for the electronic molar specific heat capacity Cy . The empirical form for this is Cy = yT and the experimentally determined value for copper is Y = 0.695 mJ mol-¹ k-². = Compare this numerical value with your result
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However,the answer of step3 (c) is not complete.Could you please complete it?Thanks

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c) The electronic molar specific heat capacity can be calculated using the formula:
C_y=YT
where Y is the electronic contribution to the heat capacity coefficient, which is related to the density
of states of the electrons at the Fermi energy. In the free electron model, Y is given by:
Y = (π^2/3) (k_B/ε_F)n
where k_B is Boltzmann's constant. Using the same values for n and _F as before, we can calculate
Y:
Y = (T^2/3) (1.38×10^-23 J/K)/(7.00 eV) (8
Transcribed Image Text:→ Step 3 c) The electronic molar specific heat capacity can be calculated using the formula: C_y=YT where Y is the electronic contribution to the heat capacity coefficient, which is related to the density of states of the electrons at the Fermi energy. In the free electron model, Y is given by: Y = (π^2/3) (k_B/ε_F)n where k_B is Boltzmann's constant. Using the same values for n and _F as before, we can calculate Y: Y = (T^2/3) (1.38×10^-23 J/K)/(7.00 eV) (8
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