Question

In adiabatic demagnetization, we use a magnetic field to couple away almost all of the residual energy of a crystal that has been cooled to 2.2 K by liquid helium. (We can get below the normal boiling point of liquid helium by boiling it at lower pressure.) Use Einstein's molar energy of the crystal, $$ E_{\mathrm{m}}=3 \mathcal{N}_A\langle\varepsilon\rangle_{\mathrm{vib}}=\frac{3 \mathcal{N}_A \omega_E}{e^{\omega / /\left(k_{\mathrm{B}} T\right)}-1} $$ in the low-temperature limit to estimate the residual molar energy of a crystal with an Einstein frequency of $105 \mathrm{~cm}^{-1}$ at 2.2 K . (The answer is smaller than you may expect.)

Name: Problem 23, Chapter 9: Physical Chemistry : Thermodynamics, Statistical Mechanics & Kinetics
Uploaded: 2022-02-24T18:34:57-08:00
Duration: 1 min 18 s
Channel: Keshav Singh

    In adiabatic demagnetization, we use a magnetic field to couple away almost all of the residual energy of a crystal that has been cooled to 2.2 K by liquid helium. (We can get below the normal boiling point of liquid helium by boiling it at lower pressure.) Use Einstein's molar energy of the crystal,

$$
E_{\mathrm{m}}=3 \mathcal{N}_A\langle\varepsilon\rangle_{\mathrm{vib}}=\frac{3 \mathcal{N}_A \omega_E}{e^{\omega / /\left(k_{\mathrm{B}} T\right)}-1}
$$

in the low-temperature limit to estimate the residual molar energy of a crystal with an Einstein frequency of $105 \mathrm{~cm}^{-1}$ at 2.2 K . (The answer is smaller than you may expect.)

Physical Chemistry : Thermodynamics, Statistical Mechanics & Kinetics

Andrew Cooksy 1st Edition

Chapter 9, Problem 23

Thanks for your feedback!

In adiabatic demagnetization, we use a magnetic field to couple away almost all of the residual energy of a crystal that has been cooled to 2.2 K by liquid helium. (We can get below the normal boiling point of liquid helium by boiling it at lower pressure.) Use Einstein's molar energy of the crystal, $$ E_{\mathrm{m}}=3 \mathcal{N}_A\langle\varepsilon\rangle_{\mathrm{vib}}=\frac{3 \mathcal{N}_A \omega_E}{e^{\omega / /\left(k_{\mathrm{B}} T\right)}-1} $$ in the low-temperature limit to estimate the residual molar energy of a crystal with an Einstein frequency of $105 \mathrm{~cm}^{-1}$ at 2.2 K . (The answer is smaller than you may expect.)