   Chapter 18, Problem 18.17E

Chapter
Section
Textbook Problem

Consider two identical planets that are the same distance from their star. One planet has an atmosphere of argon gas, and the other has an atmosphere of fluorine gas. Assume that all other physical descriptions of the planets are the same. From statistical thermodynamic perspectives, which planet should have the higher atmospheric temperature? Justify your answer by citing specific equations from the chapter.

Interpretation Introduction

Interpretation:

The planet from the given two planets that has higher atmospheric temperature is to be identified. The validation of the corresponding answer by citing specific equations is to be stated.

Concept introduction:

A molecule is made up of atoms that are bonded together by covalent bonds. These bonds undergo a to and fro movement to vibrate. This vibration of the molecule contributes to the overall partition function of the system. The vibrational temperature of a diatomic gas is given as,

θv=hvk

Where,

k represents the Boltzmann constant with value 1.381×1023J/K.

T represents the temperature (K).

v represents the ith vibrational frequency.

Explanation

According to statistical thermodynamics, the total energy of the system is given by the sum of all types of energy. The formula of energy is represented as,

E=Etrans+Eelect+Evib+Erot+Enuc

Where,

Etrans represents the translation energy.

Eelect represents the electronic energy.

Evib represents the vibrational energy.

Erot represents the rotational energy.

Enuc represents the nuclear energy.

The molecular partition function is represented as,

Q=qtransqelectqvibqrotqnuc

Where,

qtrans represents the translation partition function.

qelect represents the electronic partition function.

qvib represents the vibrational partition function

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