An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Chapter B.5, Problem 21P
To determine
To Derive: The expression of heat capacity
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In a fully degenerate gas, all the particles have energies lower than the Fermi energy.
Using the provided equation for the Fermi energy (EF), and assuming a white dwarf star has a temperature T = 107 K and a mass M = 1Msun, evaluate numerically the ratio Eth/EF, where Eth is the characteristic thermal energy of an electron in a gas of temperature T, to prove that the electrons inside a white dwarf are indeed degenerate.
(Hint: Estimate the characteristic density (ne) based on the given conditions inside a white dwarf)
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Chapter B Solutions
An Introduction to Thermal Physics
Ch. B.1 - Sketch an antiderivative of the function ex2.Ch. B.1 - Prob. 2PCh. B.1 - Prob. 3PCh. B.1 - Prob. 4PCh. B.1 - Prob. 5PCh. B.1 - Prob. 6PCh. B.2 - Prob. 7PCh. B.2 - Prob. 8PCh. B.2 - Prob. 9PCh. B.3 - Prob. 10P
Ch. B.3 - Prob. 11PCh. B.3 - Prob. 12PCh. B.3 - Prob. 13PCh. B.4 - Prob. 14PCh. B.4 - Prob. 15PCh. B.4 - Derive a formula for the volume of a d-dimensional...Ch. B.5 - Derive the general integration formulas B.36Ch. B.5 - Prob. 18PCh. B.5 - Prob. 19PCh. B.5 - Evaluate equation B.41 at x=/2, to obtain a famous...Ch. B.5 - Prob. 21PCh. B.5 - Prob. 22P
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- Consider a free Fermi gas in two dimensions, confined to a squarearea A = L2. Because g(€) is a constant for this system, it is possible to carry out the integral 7.53 for the number of particles analytically. Do so, and solve for μ as a function of N. Show that the resulting formula has the expected qualitative behavior.arrow_forwardTo obtain a more clearly defined picture of the FermiDirac distribution, consider a system of 20 FermiDirac particles sharing 94 units of energy. By drawing diagrams like Figure P10.11, show that there are nine different microstates. Using Equation 10.2, calculate and plot the average number of particles in each energy level from 0 to 14E. Locate the Fermi energy at 0 K on your plot from the fact that electrons at 0 K fill all the levels consecutively up to the Fermi energy. (At 0 K the system no longer has 94 units of energy, but has the minimum amount of 90E.) 1 Microstate8 others? One of the nine equally probable microstates for 20 FD particles with a total energy of 94E.arrow_forwardSuppose you have an ideal gas of fermions at room temperature (293 K). How large must E EF be for Fermi-Dirac and Maxwell-Boltzmann statistics to agree to within 1%? Do you think the agreement is within 1% for ideal gases under normal conditions?arrow_forward
- Let f (e) be the Fermi Dirac distribution function and U be the chemical potential. Obtain the expression for derivative of f (e) with respect to e at e=uarrow_forwardCalculate the surface density of the lattice atoms that lie on the (100) plane of a BCC crystal??? Please solve it quickly by handwrittenarrow_forwardAssume a hydrogen atom is a sphere with diameter 0.100 nm and a hydrogen molecule consists of two such spheres in contact. (a) What fraction of the space in a tank of hydrogen gas at 0°C and 1.00 atm is occupied by the hydrogen molecules themselves? (b) What fraction of the space within one hydrogen atom is occupied by its nucleus, of radius 1.20 fm?arrow_forward
- For an Einstein solid with each of the following values of Nand q, list all of the possible microstates, count them, and verify formula 2.9. N = 4, q = 2arrow_forwardTin (Sn) has a superconductive critical temperature Tc = 3.7 K and critical magnetic field at T = 0 K equal to Bc = 31 mT. What is the maximum magnetic field Sn can sustain at the critical temperature without losing its superconducting state? What is the minimum radius required for an infinite linear wire of Sn if it is to carry a current of 200 A at T = 3.0 K whilst still in its superconducting state?arrow_forwardCalculate the effective density of states for electrons and holes and intrinsic carrier concentration in GaAs at 100 °C. Here, the bandgap is assumed to show no dependence on the temperature.arrow_forward
- Calculate the number of microstates that are available in a single atom of carbon in graphite.The standard molar entropy (S°) of carbon is 5.7 J/(mol · K) and the Boltzmann constant (kB) is1.381 × 10 ―23?/?. HELP PLEASEarrow_forwardFor a system of fermions at room temperature, compute the probability of a single-particle state being occupied if its energy is. 1 eV less than μarrow_forwardCalculate the Fermi energy and electron concentration at room temperature 300Karrow_forward
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