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An Introduction to Thermal Physics
Found in: Page 220
An Introduction to Thermal Physics

An Introduction to Thermal Physics

Book edition 1st
Author(s) Daniel V. Schroeder
Pages 356 pages
ISBN 9780201380279

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Short Answer

The analysis of this section applies also to linear polyatomic molecule for which no rotation about the axis of symmetry is possible .An example is CO2, with e=0.000049 eV. Estimate the rotational partition function for a CO2 molecule at room temperature.(Note that the arrangement of the atom is OCO, and the two oxygen atoms are identical.)

Zrot =kT/2∈

=263.78

=264

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Step by Step Solution

TABLE OF CONTENTS :
TABLE OF CONTENTS

substitute 8.617*10-3 eV for k,300K for T and 0.000049eV for ∈

Here, k is Boltzmann's constant, T is the room temperature, and ∈ is a constant which sets energy scale for rotational excitations.

Zmol =kT/2∈

=(8.617*10-3-eV)(300K)/2(0.000049eV)

=263.78

=264

Most popular questions for Physics Textbooks

For a diatomic gas near room temperature, the internal partition function is simply the rotational partition function computed in section 6.2, multiplied by the degeneracy Ze of the electronic ground state.

(a) Show that the entropy in this case is

S=NkInVZeZrotNvQ+72.

Calculate the entropy of a mole of oxygen at room temperature and atmospheric pressure, and compare to the measured value in the table at the back of this book.

(b) Calculate the chemical potential of oxygen in earth's atmosphere near sea level, at room temperature. Express the answer in electron-volts

At very high temperatures (as in the very early universe), the proton and the neutron can be thought of as two different states of the same particle, called the "nucleon." (The reactions that convert a proton to a neutron or vice versa require the absorption of an electron or a positron or a neutrino, but all of these particles tend to be very abundant at sufficiently high temperatures.) Since the neutron's mass is higher than the proton's by 2.3 x 10-30 kg, its energy is higher by this amount times c2. Suppose, then, that at some very early time, the nucleons were in thermal equilibrium with the rest of the universe at 1011 K. What fraction of the nucleons at that time were protons, and what fraction were neutrons?

Apply the result of Problem 6.18 to obtain a formula for the standard deviation of the energy of a system of N identical harmonic oscillators (such as in an Einstein solid), in the high-temperature limit. Divide by the average energy to obtain a measure of the fractional fluctuation in energy. Evaluate this fraction numerically for N = 1, 104, and 1020. Discuss the results briefly.

Estimate the temperature at which the translational motion of a nitrogen molecule will freeze out, in a box of width 1 cm.

For a mole nitrogen (N2) gas at room temperature and atmospheric pressure, compute the following U,H,F,G,S and μ . (The electronic ground state of nitrogen is not degenerate.)
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