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1 Quadrature Debye's formula for the heat capacity of a solid is Cv = 9g(u) kN, (1) where the function g(u) is defined as p1/u 1¹e² 2³ Sol (e² - 17² d g(u) = y³ (2) 1)2 0 and where the terms in this equation are: N = number of particles (atoms) in the solid, k = Boltzmann constant, k = 1.38-10-23 m² kg s-2 K-¹ u = T/OD, (dimensionless temperature), T = absolute temperature in kelvin, OD = Debye temperature, which is a property specific to the solid. (a) Compute just g(u) using Eqn. 2, from u = 0 to 1.0 in intervals of 0.05 and plot the results. You should get something like the curve given in https://en.wikipedia. org/wiki/Debye_model#/media/File:DebyeVSEinstein.jpg. What happens when u is exactly zero? How big does u need to be before we do not hit a singularity? (b) Now find the isochoric heat capacity, Cu, of iron, Fe, at a temperature of T = 300K in appropriate units. Hint: You will find the Debye temperatures, Op, for various solids listed at https: //en.wikipedia.org/wiki/Debye_model. You will also need the density of iron, and the molecular weight in order to find N which is the number of Fe atoms in 1 cm³. These are easy to find in tables or on the internet. You can test your algorithm on the fact that C 3.537 J/cm³/K. Value from https://en.wikipedia.org/wiki/Table_of_specific_heat_capacities. dz,

1 Quadrature Debye's formula for the heat capacity of a solid is Cv = 9g(u) kN, (1) where the function g(u) is defined as p1/u 1¹e² 2³ Sol (e² - 17² d g(u) = y³ (2) 1)2 0 and where the terms in this equation are: N = number of particles (atoms) in the solid, k = Boltzmann constant, k = 1.38-10-23 m² kg s-2 K-¹ u = T/OD, (dimensionless temperature), T = absolute temperature in kelvin, OD = Debye temperature, which is a property specific to the solid. (a) Compute just g(u) using Eqn. 2, from u = 0 to 1.0 in intervals of 0.05 and plot the results. You should get something like the curve given in https://en.wikipedia. org/wiki/Debye_model#/media/File:DebyeVSEinstein.jpg. What happens when u is exactly zero? How big does u need to be before we do not hit a singularity? (b) Now find the isochoric heat capacity, Cu, of iron, Fe, at a temperature of T = 300K in appropriate units. Hint: You will find the Debye temperatures, Op, for various solids listed at https: //en.wikipedia.org/wiki/Debye_model. You will also need the density of iron, and the molecular weight in order to find N which is the number of Fe atoms in 1 cm³. These are easy to find in tables or on the internet. You can test your algorithm on the fact that C 3.537 J/cm³/K. Value from https://en.wikipedia.org/wiki/Table_of_specific_heat_capacities. dz,

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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1 Quadrature Debye's formula for the heat capacity of a solid is Cv = 9g(u) kN, (1) where the function g(u) is defined as p1/u 1¹e² 2³ Sol (e² - 17² d g(u) = y³ (2) 1)2 0 and where the terms in this equation are: N = number of particles (atoms) in the solid, k = Boltzmann constant, k = 1.38-10-23 m² kg s-2 K-¹ u = T/OD, (dimensionless temperature), T = absolute temperature in kelvin, OD = Debye temperature, which is a property specific to the solid. (a) Compute just g(u) using Eqn. 2, from u = 0 to 1.0 in intervals of 0.05 and plot the results. You should get something like the curve given in https://en.wikipedia. org/wiki/Debye_model#/media/File:DebyeVSEinstein.jpg. What happens when u is exactly zero? How big does u need to be before we do not hit a singularity? (b) Now find the isochoric heat capacity, Cu, of iron, Fe, at a temperature of T = 300K in appropriate units. Hint: You will find the Debye temperatures, Op, for various solids listed at https: //en.wikipedia.org/wiki/Debye_model. You will also need the density of iron, and the molecular weight in order to find N which is the number of Fe atoms in 1 cm³. These are easy to find in tables or on the internet. You can test your algorithm on the fact that C 3.537 J/cm³/K. Value from https://en.wikipedia.org/wiki/Table_of_specific_heat_capacities. dz,
Transcribed Image Text:1 Quadrature Debye's formula for the heat capacity of a solid is Cv = 9g(u) kN, (1) where the function g(u) is defined as p1/u 1¹e² 2³ Sol (e² - 17² d g(u) = y³ (2) 1)2 0 and where the terms in this equation are: N = number of particles (atoms) in the solid, k = Boltzmann constant, k = 1.38-10-23 m² kg s-2 K-¹ u = T/OD, (dimensionless temperature), T = absolute temperature in kelvin, OD = Debye temperature, which is a property specific to the solid. (a) Compute just g(u) using Eqn. 2, from u = 0 to 1.0 in intervals of 0.05 and plot the results. You should get something like the curve given in https://en.wikipedia. org/wiki/Debye_model#/media/File:DebyeVSEinstein.jpg. What happens when u is exactly zero? How big does u need to be before we do not hit a singularity? (b) Now find the isochoric heat capacity, Cu, of iron, Fe, at a temperature of T = 300K in appropriate units. Hint: You will find the Debye temperatures, Op, for various solids listed at https: //en.wikipedia.org/wiki/Debye_model. You will also need the density of iron, and the molecular weight in order to find N which is the number of Fe atoms in 1 cm³. These are easy to find in tables or on the internet. You can test your algorithm on the fact that C 3.537 J/cm³/K. Value from https://en.wikipedia.org/wiki/Table_of_specific_heat_capacities. dz,
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