An ideal gas of N spin (1)/(2) fermions is confined to a volume V. Calculate the zero temperatur

Step 1: **Calculate the chemical potential at zero temperature.**u000Au000AAt zero temperature, the chem

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An ideal gas of $N \operatorname{spin} \frac{1}{2}$ fermions is confined to a volume $V$. Calculate the zero temperature limit of (a) the chemical potential, (b) the average energy per particle, (c) the pressure, (d) the Pauli spin susceptibility. Show that in Gaussian units the susceptibility can be written as $3 \mu_{\mathrm{B}}^2 N / 2 \mu(0) V$, where $\mu(0)$ is the chemical potential at zero temperature. Assume each fermion has interaction with an external magnetic field of the form $2 \mu_0 H S_z$, where $\mu_{\mathrm{B}}$ is the Bohr magneton and $S_z$ is the $z$-component of the spin.

   An ideal gas of $N \operatorname{spin} \frac{1}{2}$ fermions is confined to a volume $V$. Calculate the zero temperature limit of (a) the chemical potential, (b) the average energy per particle, (c) the pressure, (d) the Pauli spin susceptibility. Show that in Gaussian units the susceptibility can be written as $3 \mu_{\mathrm{B}}^2 N / 2 \mu(0) V$, where $\mu(0)$ is the chemical potential at zero temperature. Assume each fermion has interaction with an external magnetic field of the form $2 \mu_0 H S_z$, where $\mu_{\mathrm{B}}$ is the Bohr magneton and $S_z$ is the $z$-component of the spin.

Problems and Solutions on Thermodynamics and Statistical Mechanics

U.S.T. of China… 1st Edition

Chapter 2, Problem 105

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Step 1

** At zero temperature, the chemical potential $\mu(0)$ for a system of $N$ spin-$\frac{1}{2}$ fermions can be determined from the Fermi energy. The Fermi energy $E_F$ is given by: \[ E_F = \frac{\hbar^2 k_F^2}{2m} \] where $k_F$ is the Fermi wave Show more…

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An ideal gas of $N \operatorname{spin} \frac{1}{2}$ fermions is confined to a volume $V$. Calculate the zero temperature limit of (a) the chemical potential, (b) the average energy per particle, (c) the pressure, (d) the Pauli spin susceptibility. Show that in Gaussian units the susceptibility can be written as $3 \mu_{\mathrm{B}}^2 N / 2 \mu(0) V$, where $\mu(0)$ is the chemical potential at zero temperature. Assume each fermion has interaction with an external magnetic field of the form $2 \mu_0 H S_z$, where $\mu_{\mathrm{B}}$ is the Bohr magneton and $S_z$ is the $z$-component of the spin.

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