Experimental measurements of the heat capacity of aluminum at low temperatures (below about 50 K) can be fit to the formula Cv = aT+bT3 ,where Cv is the heat capacity of one mole of aluminum, and the constants a and b are approximately a = 0.00135 J/K2 and b = 2.48 X 10-5 J/K4. From this data, find a formula for the entropy of a mole of aluminum as a function of temperature. Evaluate your formula at T = 1 K and at T = 10 K, expressing your answers both in conventional units (J/K) and as unitless numbers (dividing by Boltzmann's constant).
Experimental measurements of the heat capacity of aluminum at low temperatures (below about 50 K) can be fit to the formula Cv = aT+bT3 ,where Cv is the heat capacity of one mole of aluminum, and the constants a and b are approximately a = 0.00135 J/K2 and b = 2.48 X 10-5 J/K4. From this data, find a formula for the entropy of a mole of aluminum as a function of temperature. Evaluate your formula at T = 1 K and at T = 10 K, expressing your answers both in conventional units (J/K) and as unitless numbers (dividing by Boltzmann's constant).
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter18: Heat Engines, Entropy, And The Second Law Of Thermodynamics
Section: Chapter Questions
Problem 36P
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Experimental measurements of the heat capacity of aluminum at low temperatures (below about 50 K) can be fit to the formula
Cv = aT+bT3 ,
where Cv is the heat capacity of one mole of aluminum, and the constants a and b are approximately a = 0.00135 J/K2 and b = 2.48 X 10-5 J/K4. From this data, find a formula for the entropy of a mole of aluminum as a function of temperature. Evaluate your formula at T = 1 K and at T = 10 K, expressing your answers both in conventional units (J/K) and as unitless numbers (dividing by Boltzmann's constant).
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