An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 2.2, Problem 7P
To determine
Representation of microstates for an Einstein solid as a series of dots and vertical lines.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Problem 3.
A pendulum is formed by suspending a mass m from the
ceiling, using a spring of unstretched length lo and spring constant k.
3.1. Using r and 0 as generalized coordinates, show that
1
L =
= 5m (i² + r²0?) + mgr cos 0 –
z* (r – lo)²
3.2. Write down the explicit equations of motion for your generalized coordinates.
Use a computer to reproduce the table and graph in Figure 2.4: two Einstein solids, each containing three harmonic oscillators, with a total of six units of energy. Then modify the table and graph to show the case where one Einstein solid contains six harmonic oscillators and the other contains four harmonic oscillators (with the total number of energy units still equal to six). Assuming that all microstates are equally likely, what is the most probable macrostate, and what is its probability? What is the least probable macrostate, and what is its probability?
Problem 3.36. Consider an Einstein solid for which both N and q are much
greater than 1. Think of each oscillator as a separate "particle."
(a) Show that the chemical potential is
N+
- kT ln
N
(b) Discuss this result in the limits N > q and N « q, concentrating on the
question of how much S increases when another particle carrying no energy
is added to the system. Does the formula make intuitive sense?
Chapter 2 Solutions
An Introduction to Thermal Physics
Ch. 2.1 - Prob. 1PCh. 2.1 - Prob. 2PCh. 2.1 - Prob. 3PCh. 2.1 - Prob. 4PCh. 2.2 - For an Einstein solid with each of the following...Ch. 2.2 - Prob. 6PCh. 2.2 - Prob. 7PCh. 2.3 - Prob. 8PCh. 2.3 - Use a computer to reproduce the table and graph in...Ch. 2.3 - Use a computer to produce a table and graph, like...
Ch. 2.3 - Use a computer to produce a table and graph, like...Ch. 2.4 - Prob. 12PCh. 2.4 - Fun with logarithms. (a) Simplify the expression...Ch. 2.4 - Write e1023 in the form 10x, for some x.Ch. 2.4 - Prob. 15PCh. 2.4 - Prob. 16PCh. 2.4 - Prob. 17PCh. 2.4 - Prob. 18PCh. 2.4 - Prob. 19PCh. 2.4 - Suppose you were to shrink Figure 2.7 until the...Ch. 2.4 - Prob. 21PCh. 2.4 - Prob. 22PCh. 2.4 - Prob. 23PCh. 2.4 - Prob. 24PCh. 2.4 - Prob. 25PCh. 2.5 - Prob. 26PCh. 2.5 - Prob. 27PCh. 2.6 - How many possible arrangements are there for a...Ch. 2.6 - Consider a system of two Einstein solids, with...Ch. 2.6 - Prob. 30PCh. 2.6 - Fill in the algebraic steps to derive the...Ch. 2.6 - Prob. 32PCh. 2.6 - Use the Sackur-Tetrode equation to calculate the...Ch. 2.6 - Prob. 34PCh. 2.6 - According to the Sackur-Tetrode equation, the...Ch. 2.6 - For either a monatomic ideal gas or a...Ch. 2.6 - Using the Same method as in the text, calculate...Ch. 2.6 - Prob. 38PCh. 2.6 - Compute the entropy of a mole of helium at room...Ch. 2.6 - For each of the following irreversible process,...Ch. 2.6 - Describe a few of your favorite, and least...Ch. 2.6 - A black hole is a region of space where gravity is...
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- I am confused with part (e). I don't understand the steps. How is 1.427 obtained? How is the 20t moved to the left side of the equation, since it is inside the COS() function? I am just not understanding the math. Can you step it through with an explanation at each individual step?arrow_forwardStarting with the equation of motion of a three-dimensional isotropic harmonic ocillator dp. = -kr, dt (i = 1,2,3), deduce the conservation equation dA = 0, dt where 1 P.P, +kr,r,. 2m (Note that we will use the notations r,, r2, r, and a, y, z interchangeably, and similarly for the components of p.)arrow_forwardBefore we introduced the Friedmann equation, we gained some intuition with a Newtonian example of an expanding sphere of uniform density that feels its own gravity. Suppose the sphere is currently static; it has expanded to its maximum size and is about to recollapse. Given that its total energy per mass is U, and its density is currently \rhoρ, what is its current size? Write your answer in meters, using one decimal place. Values: U = -82 J/kg \rhoρ = 545 x 105 kg/m3 Please show work as I have trouble following alongarrow_forward
- Hello, I need help solving for the missing data for Table 6.2 with explanations. I provided the equations I am working with. Please and thank you.arrow_forwardCalculate the (relativistic) minimum kinetic energy of an electron confined to a carbon nucleus, which can be modeled as a sphere of radius 2.7 fm. Sketch the situation, defining all of your variablesarrow_forwardConsider the function v(t) = 6 – t. (a) Write out the four terms of the right Riemann sum for v with four subdivisions on the interval [-1,7]. (b) Does your sum estimate the area or the signed area between the graph of v, r-axis, t = -1, and t = 7? Explain. (c) If v represented the velocity due east (in mph) as a function of time (in hours), use terms in your Riemann sum to estimate i. distance travelled on the interval [–1,7]. ii. total displacement on the interval [–1,7].arrow_forward
- Consider the Kepler equation of motion M = E − e sin (E) Where : M – mean anomaly E – eccentric anomaly of an elliptic orbit e – eccentricity To find E, we need to solve the nonlinear equation: f(E) = M + e sin(E ) − E = 0 Given e = 0.0167 (Earth’s eccentricity)and M = 1 (in radians) compute E using a. Secant Method All with Ea ≤ 0.00001 To choose appropriate initial approximations or an interval containing the root, plot the function f(E) and then determine graphically where it crosses the E-axis.arrow_forwardFind an equation for the plane through the points (-6, 8, – 1) and (-1,3, –8) and perpendicular to the plane -4x – 3y + 8z = 10. An equation for the plane is ...arrow_forwardThe Newton–Raphson method for finding the stationary point(s) Rsp of a potential energy surface V is based on a Taylor-series expansion around a guess, R0. Similarly, the velocity Verlet algorithm for integrating molecular dynamics trajectories [xt, vt] is based on a Taylor-series expansion around the initial conditions, [x0, v0]. Both of these methods rely strictly on local information about the system. How many derivatives do we need to compute in order to apply them?arrow_forward
- please help me with problem 3.1. Please explain it and solve step by step solutions. thank you!arrow_forwardProblem 3: Chemical potential of an Einstein solid. Consider an Einstein solid for which both N and q are much greater than 1. Think of each ocillator as a separate “particle". a) Show that the chemical potential is H = -kT In (**e) b) Discuss this result in the limits N » q and N « q, concentrating on the question of how much S increases when another particle carrying no energy is added to the system. Does the formula make intuitive sense?arrow_forwardConsider the half oscillator" in which a particle of mass m is restricted to the region x > 0 by the potential energy U(x) = 00 for a O where k is the spring constant. What are the energies of the ground state and fırst excited state? Explain your reasoning. Give the energies in terms of the oscillator frequency wo = Vk/m. Formulas.pdf (Click here-->)arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
University Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSON
Introduction To Quantum MechanicsPhysicsISBN:9781107189638Author:Griffiths, David J., Schroeter, Darrell F.Publisher:Cambridge University Press
Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Lecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...PhysicsISBN:9780134609034Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart FieldPublisher:PEARSON
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON