Chemical Thermodynamics and Physical Transformations : please show step by step how each section is derived. 1. Show that the partition function for a harmonic oscillator in the x direction only is given by:9xexp(-ẞhy)1-exp(-ẞhv)2. Using your answer to part (1), derive the partition function for a single harmonic oscillator in three differentdirections. Briefly note any assumptions made.3. Using your answer to part (2), show that the partition function for a crystal of n atoms (i.e., a collection ofharmonic oscillators in three different directions) is given by:3Nexp(-ẞhv)Qays1-exp(-ẞhv)

We can derive the vibrational partition function in one dimension taking simple harmonic oscillator…

Answered: 1. Show that the partition function for…

1. Show that the partition function for a harmonic oscillator in the x direction only is given by: exp(-ẞhv) qx 1-exp(-ẞhv)

Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter17: Statistical Thermodynamics: Introduction

Section: Chapter Questions

Problem 17.13E

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Question

Chemical Thermodynamics and Physical Transformations : please show step by step how each section is derived.

1. Show that the partition function for a harmonic oscillator in the x direction only is given by:
9x
exp(-ẞhy)
1-exp(-ẞhv)
2. Using your answer to part (1), derive the partition function for a single harmonic oscillator in three different
directions. Briefly note any assumptions made.
3. Using your answer to part (2), show that the partition function for a crystal of n atoms (i.e., a collection of
harmonic oscillators in three different directions) is given by:
3N
exp(-ẞhv)
Qays
1-exp(-ẞhv)

Science that deals with the amount of energy transferred from one equilibrium state to another equilibrium state.

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