Solution Found!
In the low-temperature limit (kT ? ?), each term in the
Chapter 6, Problem 26P(choose chapter or problem)
Problem 26P
In the low-temperature limit (kT ≪ ϵ), each term in the rotational partition function (equation is much smaller than the one before. Since the first term is independent of T, cut off the sum after the second term and compute the average energy and the heat capacity in this approximation. Keep only the largest T-dependent term at each stage of the calculation. Is your result consistent with the third law of thermodynamics? Sketch the behaviour of the heat capacity at all temperatures, interpolating between the high-temperature and low-temperature expressions.
equation
Questions & Answers
QUESTION:
Problem 26P
In the low-temperature limit (kT ≪ ϵ), each term in the rotational partition function (equation is much smaller than the one before. Since the first term is independent of T, cut off the sum after the second term and compute the average energy and the heat capacity in this approximation. Keep only the largest T-dependent term at each stage of the calculation. Is your result consistent with the third law of thermodynamics? Sketch the behaviour of the heat capacity at all temperatures, interpolating between the high-temperature and low-temperature expressions.
equation
ANSWER:
Step 1 of 4
The rotational partition function of the system is given as follows
Here, 
