Molar Heat Capacity of Potassium Alum KAl(SO4)2 ·12H2O at Low Temperatures: Revisited with Determination of the Debye Temperature

Kwang Sei Lee; Cheol Eui Lee

doi:10.3938/jkps.72.379

Molar Heat Capacity of Potassium Alum KAl(SO₄)₂ ·12H₂O at Low Temperatures: Revisited with Determination of the Debye Temperature

Kwang Sei Lee, Cheol Eui Lee

Department of Physics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

Two earlier published experimental data [C. H. Shomate, J. Am. Chem. Soc. 67, 765 (1945); D. G. Kapadnis and R. Hartmans, Physica 22, 173 (1956)] of the molar heat capacity C_p of potassium alum, KAl(SO₄)₂·12H₂O, are revisited. From analysis of the temperature dependence of C_p [D. G. Kapadnis and R. Hartmans, Physica 22, 173 (1956)] below 20 K by using the experimental values of C_p represented as a plot of C_p/T = γ+AT², the Sommerfeld parameter γ (electronic heat capacity coefficient) and the slope A (lattice heat capacity coefficient) are estimated as γ = 0 JK ⁻²mol ⁻¹ and A = 3.35×10 ⁻³ JK ⁻⁴mol ⁻¹, respectively. This indicates that only acoustic phonons contribute to the heat capacity below 4 K. The Debye T³-law is found to hold good to 4 K, i.e., to T < θ_D/20, where θ_D is the calorimetric Debye temperature calculated as θ_D = 83.4 K, indicative of the strength of the chemical bonding in the system.

Original language	English
Pages (from-to)	379-383
Number of pages	5
Journal	Journal of the Korean Physical Society
Volume	72
Issue number	3
DOIs	https://doi.org/10.3938/jkps.72.379
Publication status	Published - 2018 Feb 1

Bibliographical note

Funding Information:
This work was supported by the National Research Foundation of Korea (Project No. 2016R1D1A1A0991 7003).

Publisher Copyright:
© 2018, The Korean Physical Society.

Keywords

Debye temperature
Heat capacity
Potassium alum

ASJC Scopus subject areas

General Physics and Astronomy

Access to Document

10.3938/jkps.72.379

Cite this

@article{19e0e46623fa4a53988b75d0287d0873,

title = "Molar Heat Capacity of Potassium Alum KAl(SO4)2 ·12H2O at Low Temperatures: Revisited with Determination of the Debye Temperature",

abstract = "Two earlier published experimental data [C. H. Shomate, J. Am. Chem. Soc. 67, 765 (1945); D. G. Kapadnis and R. Hartmans, Physica 22, 173 (1956)] of the molar heat capacity Cp of potassium alum, KAl(SO4)2·12H2O, are revisited. From analysis of the temperature dependence of Cp [D. G. Kapadnis and R. Hartmans, Physica 22, 173 (1956)] below 20 K by using the experimental values of Cp represented as a plot of Cp/T = γ+AT2, the Sommerfeld parameter γ (electronic heat capacity coefficient) and the slope A (lattice heat capacity coefficient) are estimated as γ = 0 JK −2mol −1 and A = 3.35×10 −3 JK −4mol −1, respectively. This indicates that only acoustic phonons contribute to the heat capacity below 4 K. The Debye T3-law is found to hold good to 4 K, i.e., to T < θD/20, where θD is the calorimetric Debye temperature calculated as θD = 83.4 K, indicative of the strength of the chemical bonding in the system.",

keywords = "Debye temperature, Heat capacity, Potassium alum",

author = "Lee, {Kwang Sei} and Lee, {Cheol Eui}",

note = "Funding Information: This work was supported by the National Research Foundation of Korea (Project No. 2016R1D1A1A0991 7003). Publisher Copyright: {\textcopyright} 2018, The Korean Physical Society.",

year = "2018",

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N2 - Two earlier published experimental data [C. H. Shomate, J. Am. Chem. Soc. 67, 765 (1945); D. G. Kapadnis and R. Hartmans, Physica 22, 173 (1956)] of the molar heat capacity Cp of potassium alum, KAl(SO4)2·12H2O, are revisited. From analysis of the temperature dependence of Cp [D. G. Kapadnis and R. Hartmans, Physica 22, 173 (1956)] below 20 K by using the experimental values of Cp represented as a plot of Cp/T = γ+AT2, the Sommerfeld parameter γ (electronic heat capacity coefficient) and the slope A (lattice heat capacity coefficient) are estimated as γ = 0 JK −2mol −1 and A = 3.35×10 −3 JK −4mol −1, respectively. This indicates that only acoustic phonons contribute to the heat capacity below 4 K. The Debye T3-law is found to hold good to 4 K, i.e., to T < θD/20, where θD is the calorimetric Debye temperature calculated as θD = 83.4 K, indicative of the strength of the chemical bonding in the system.

AB - Two earlier published experimental data [C. H. Shomate, J. Am. Chem. Soc. 67, 765 (1945); D. G. Kapadnis and R. Hartmans, Physica 22, 173 (1956)] of the molar heat capacity Cp of potassium alum, KAl(SO4)2·12H2O, are revisited. From analysis of the temperature dependence of Cp [D. G. Kapadnis and R. Hartmans, Physica 22, 173 (1956)] below 20 K by using the experimental values of Cp represented as a plot of Cp/T = γ+AT2, the Sommerfeld parameter γ (electronic heat capacity coefficient) and the slope A (lattice heat capacity coefficient) are estimated as γ = 0 JK −2mol −1 and A = 3.35×10 −3 JK −4mol −1, respectively. This indicates that only acoustic phonons contribute to the heat capacity below 4 K. The Debye T3-law is found to hold good to 4 K, i.e., to T < θD/20, where θD is the calorimetric Debye temperature calculated as θD = 83.4 K, indicative of the strength of the chemical bonding in the system.

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