An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
expand_more
expand_more
format_list_bulleted
Question
Chapter 3.3, Problem 20P
To determine
The energy, magnetization, and entropy of the system and along with the method experimenters have to do to attain 99% of the maximum possible magnetization.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Consider an ideal two-state electronic paramagnet such as DPPH,with µ = µB. In the experiment described above, the magnetic field strength was 2.06 T and the minimum temperature was 2.2 K. Calculate the energy, magnetization, and entropy of this system, expressing each quantity as a fraction of its maximum possible value. What would the experimenters have had to do to attain 99% of the maximum possible magnetization?
The Einstein model for a solid assumes the system consists of 3N independent simple harmonic oscillators with frequencies &. Within these assumptions, the heat capacity at constant volume as:
Cv=3Nk() (-1)²
²
Complete the table for the molar heat capacity at various temperatures under either the Einstein model or high-temperature limit. You might like to use the Wolfram Alpha calculator to do the numerical calculations more
easily. Use k-0.695 cm /K.
High temperature limit value of molar heat capacity of metal is
T
1 K
10 K
50 K
-1
Einstein, = 100 cm Einstein, : = 500 cm
1.4021
3.8991
100 K
500 K
2.434E-4
1000 K
6.1499
2434E-4
kJ/mol.
Show that the entropy of a two-state paramagnet, expressed asa function of temperature, is S = Nk [ln(2coshx) -x tanh x], where x = µB/kT.Check that this formula has the expected behavior as T → 0 and T → ∞ .
Chapter 3 Solutions
An Introduction to Thermal Physics
Ch. 3.1 - Use Table 3.1 to compute the temperature of solid...Ch. 3.1 - Use the definition of temperature to prove the...Ch. 3.1 - Figure 3.3 shows graphs of entropy vs. energy for...Ch. 3.1 - Can a miserly system, with a concave-up...Ch. 3.1 - Prob. 5PCh. 3.1 - Prob. 6PCh. 3.1 - Prob. 7PCh. 3.2 - Prob. 8PCh. 3.2 - In solid carbon monoxide, each CO molecule has two...Ch. 3.2 - An ice cube (mass 30 g) at 0C is left sitting on...
Ch. 3.2 - In order to take a nice warm bath, you mix 50...Ch. 3.2 - Estimate the change in the entropy of the universe...Ch. 3.2 - When the sun is high in the sky, it delivers...Ch. 3.2 - Experimental measurements of the heat capacity of...Ch. 3.2 - Prob. 15PCh. 3.2 - A bit of computer memory is some physical object...Ch. 3.3 - Prob. 17PCh. 3.3 - Prob. 18PCh. 3.3 - Prob. 19PCh. 3.3 - Prob. 20PCh. 3.3 - Prob. 21PCh. 3.3 - Prob. 22PCh. 3.3 - Prob. 23PCh. 3.3 - Prob. 24PCh. 3.3 - Prob. 25PCh. 3.3 - Prob. 26PCh. 3.4 - What partial-derivative relation can you derive...Ch. 3.4 - A liter of air, initially at room temperature and...Ch. 3.4 - Sketch a qualitatively accurate graph of the...Ch. 3.4 - As shown in Figure 1.14, the heat capacity of...Ch. 3.4 - Experimental measurements of heat capacities are...Ch. 3.4 - A cylinder contains one liter of air at room...Ch. 3.4 - Prob. 33PCh. 3.4 - Polymers, like rubber, are made of very long...Ch. 3.5 - Prob. 35PCh. 3.5 - Prob. 36PCh. 3.5 - Prob. 37PCh. 3.5 - Suppose you have a mixture of gases (such as air,...Ch. 3.6 - Prob. 39P
Knowledge Booster
Similar questions
- Consider N identical harmonic oscillators (as in the Einstein floor). Let the allowed energies of each oscillator (E = n h f (n = 0, 1, 2 ...)) 0, hf, 2hf and so on. A) Find the Helmholtz free energy of this system. B) Derive the expression that gives the entropy of this system as a function of temperature.arrow_forwardAsystem consist of 5 indistinguishable particles, the total energy U=8£ , the degenerey gi = 4 for each energy level, the distribution of the particles on the energy levels shows in the figure (note that, there is no restriction on the number of particles on each energy state and there is no zeroth energy level). Calculate the entropy of the system( K3=8.62 x10 eVK'). k 1 2 3 4 5 6 N . EYE 4 3 2 . 1 :: .. w 5.59 x10-4 eVK-140 6.59 x10-5 eVK-1 80 7.59 x10-6 eVK-1.00arrow_forwardIf levels 1 and 2 are separated by an energy E2 – E1 such that the corresponding transition frequency falls in the middle of the visible range, calculate the ratio of the populations of the two levels in thermal equilibrium at room temperature and hence interpret the results physically?arrow_forward
- Consider a model thermodynamic assembly in which the allowed (non-degenerate) one-particle states have energies 0, (epsilon), 2(epsilon), 3(epsilon), 4(epsilon), .... The assembly has four distinguishable (localized) particles and a total energy of 6(epsilon). Identify all possible distributions, and evaluate the entropy of the most probable and the least probable distributions of the four particles in the energy states.arrow_forwardIn a canonical ensemble, how does the entropy relate to the thermodynamic probabilities of various energy states? Mention the significance of the said relation. I want handwritten solution only.....arrow_forwardFind an explicit relation for the chemical potential u of a 2DEG at a finite temperature.arrow_forward
- The first excited energy level of a hydrogen atom has an energy of10.2 eV, if we take the ground-state energy to be zero. However, the first excited level is really four independent states, all with the same energy. We can therefore assign it an entropy of 8 = kIn 4, since for this given value of the energy, the multiplicity is 4. Question: For what temperatures is the Helmholtz free energy of a hydrogen atom in the first excited level positive, and for what temperatures is it negative?arrow_forward(a) The mean free path for a classical gas is 1 l = Nad' give a heuristic derivation of the mean free path explaining all the terms and any assump- tions made. (b) The Boltzmann transport equation for a classical distribution function is +ở .V7ƒ +ã · Võƒ = collisions Briefly sketch how it is derived and explain the terms. (c) Explain the significance of the relaxation time Te, and use the relaxation time approxi- mation to rewrite the Boltzmann transport equatio.arrow_forward9.1. Consider the results for ideal gases derived from quantum mechanics. Write an expression for the function s(T, v) that includes the parameter A(T). (a) Show that the behavior of the entropy as T0 is unrealistic in a quantum sense. What approximation in the derivation is responsible for this behavior? (b) The Sackur-Tetrode equation is valid when the thermal de Broglie wave- length is much less than the average molecular separation distance, A(T) < (V/N)13, which is generally the case at high temperatures. Calculate the temperature at which this inequality is first violated for an ideal gas at atmospheric pressure and with a mass of 6.6 × 10-26 kg/molecule (which is typical of argon). xarrow_forward
- a) Show that for enthalpy and Gibbs free energy, H = G + TS can be written. b) Based on the exact differential of Gibbs free energyarrow_forwardFor an ideal gas of classical non- interacting atoms in thermal equilibrium, the Cartesian component of the velocity are statistically independent. In three dimensions, the probability density distribution of the velocity is: where σ² = kBT m P(Vx, Vy, Vz) = (2nо²)-³/² exp 20² 1. Show that the probability density of the velocity is normalized. 2. Find an expression of the arithmetic average of the speed. 3. Find and expression of the root-mean-square value of the speed. 4. Estimate the standard deviation of the speed.arrow_forwardSuppose we are in the NPT ensemble, and that the entropy S = S(L) depends on the length of a molecule. We also find that S(L) = -3L. Given that dG = -SdT + Vdp + μdN + fdL, what does (∂f/∂T)L equal when L is 2?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning