In crystalline solids, atoms are arranged in periodic arrays. The atoms themselves are fixed in place but can vibrate. You can imagine that the atoms in a crystal behave as if they are connected to their neighbors by springs. These vibrations travel as waves called “phonons” (lattice vibrations). The heat capacity of a crystalline solid arises from these vibrational degrees of freedom and is described mathematically by the Debye law: Where N = Avogadro’s number, k = Boltzmann’s constant, and θ is the Debye temperature a constant that is a metric of the stiffness of the “springs” and is correlated with mechanical properties of solids (i.e., mechanically softer solids tend to exhibit lower θ). a. Calculate the change in entropy associated with changing the temperature of diamond from 15 K to 100 K. (θ = 2230 K) b. The Debye temperature of gold (Au) is θ = 170 K. Calculate the entropy change associated with changing the temperature of solid gold from 15 K to 100 K. c. Compare your values from a) and b). Provide an explanation for the differences in entropy of this process for diamond vs. gold.
In crystalline solids, atoms are arranged in periodic arrays. The atoms themselves are fixed in place but can vibrate. You can imagine that the atoms in a crystal behave as if they are connected to their neighbors by springs. These vibrations travel as waves called “phonons” (lattice vibrations). The heat capacity of a crystalline solid arises from these vibrational degrees of freedom and is described mathematically by the Debye law: Where N = Avogadro’s number, k = Boltzmann’s constant, and θ is the Debye temperature a constant that is a metric of the stiffness of the “springs” and is correlated with mechanical properties of solids (i.e., mechanically softer solids tend to exhibit lower θ). a. Calculate the change in entropy associated with changing the temperature of diamond from 15 K to 100 K. (θ = 2230 K) b. The Debye temperature of gold (Au) is θ = 170 K. Calculate the entropy change associated with changing the temperature of solid gold from 15 K to 100 K. c. Compare your values from a) and b). Provide an explanation for the differences in entropy of this process for diamond vs. gold.
In crystalline solids, atoms are arranged in periodic arrays. The atoms themselves are fixed in place but can vibrate. You can imagine that the atoms in a crystal behave as if they are connected to their neighbors by springs.
These vibrations travel as waves called “phonons” (lattice vibrations). The heat capacity of a crystalline solid arises from these vibrational degrees of freedom and is described mathematically by the Debye law:
Where N = Avogadro’s number, k = Boltzmann’s constant, and θ is the Debye temperature a constant that is a metric of the stiffness of the “springs” and is correlated with mechanical properties of solids (i.e., mechanically softer solids tend to exhibit lower θ).
a. Calculate the change in entropy associated with changing the temperature of diamond from 15 K to 100 K. (θ = 2230 K)
b. The Debye temperature of gold (Au) is θ = 170 K. Calculate the entropy change associated with changing the temperature of solid gold from 15 K to 100 K.
c. Compare your values from a) and b). Provide an explanation for the differences in entropy of this process for diamond vs. gold.
Definition Definition Number of atoms/molecules present in one mole of any substance. Avogadro's number is a constant. Its value is 6.02214076 × 10 23 per mole.
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World of Chemistry, 3rd editionChemistryISBN:9781133109655Author:Steven S. Zumdahl, Susan L. Zumdahl, Donald J. DeCostePublisher:Brooks / Cole / Cengage Learning