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 2.6, Problem 30P
(a)
To determine
To Find: The entropy of the combined system of two identical Einstein solids.
(b)
To determine
To Find: The entropy of the combined system of two identical Einstein solids and the system is in its most likely macrostate.
(c)
To determine
To Explain: The relevancy of the time scale to the entropy of the combined system.
(d)
To determine
To Explain: Is there any violation of second law of
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Consider a van der Waal's gas that undergoes an
isothermal expansion from volume V₁ to volume V₂.
Calculate the change in the Helmholtz free energy.
2.2
(a)
(b)
From the theory of thermodynamics, with T and V
T
independent, ()₁ = T()-p. Show that the change in
internal energy is AU = a(-1/2).
The multiplicity of an Einstein solid can be approximated as: given png
for N oscillators and q energy units. The internal energy of the system is U=qϵ, where ϵ is some constant. Find an expression for the entropy of an Einstein solid as a function of N and q. Use this expression to derive temperature as a function of energy, U. Take your derivation a step further, and determine the formula for heat capacity using T(U,N). Show that as T goes to ∞, the heat capacity becomes C=Nk. (Consider when x is small, ex~1+x.) Does this make sense? Explain your logic and steps.
Problem 4.1. Recall Problem 1.34, which concerned an ideal diatomic gas taken around a rectangular cycle on a PV diagram. Suppose now that this system is used as a heat engine, to convert the heat added into mechanical work. (a) Evaluate the efficiency of this engine for the case V2 = 3V1, P2 = 2P1. (b) Calculate the efficiency of an "ideal" engine operating between the same temperature extremes.
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
- Statical Mechanics (Thermal and Statical Physics) Instruction: Write ALL the solutions of this (necessary or and not direct answer). Write also the equations that are needed to solve for a certain problem. Thank you. Problem: Now, we have the number of microstates and in between E and E + ∆E in isolated system of N particles in the volume V is given by: (Please see the image attached) Where a,b, c are constants. Note: Answer also letter A-Darrow_forwardProve that the entropy S of an ideal gas [Sackur and Tetrode's equation] is an extensive quantity. Then show that the entropy of the gas of particles to be separated from each other is 3 S = NKB — Nku [2 - In (2/V)], and that this quantity is not extensive. Remember: by extensiveness we mean that if we scale the size of the system by a factor a (V → a V, N a N, but the particle density n = N/V remains constant), any extensive quantity a s) also scales by a factor a (here: S →arrow_forwardLet Ω be a new thermodynamic potential that is a “natural” function of temperature T, volume V, and the chemical potential μ. Provide a definition of Φ in the form of a Legendre transformation and also write its total differential, or derived fundamental equation, in terms of these natural variables.arrow_forward
- 3.2 When the number of particles changes in a thermodynamic transformation, it is important to use the correct form of entropy for an ideal gas, as given by the Sacker-Tetrode equation (2.49). (a) Use the Sacker-Tetrode equation to calculate A(V, T) and G(P, T) for an ideal gas. Show, in particular, that A(V,T) = NkT[In(nλ³) — 1], where it is the density, and λ = √2h²/mkT is the thermal wavelength. (b) Obtain the chemical potential for an ideal gas from (2A/3N)v.7 and (ƏG/AN)P.T. Show that you get the same answer μ = KT ln(nλ³).arrow_forwardConsider 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_forwardT04.2 Atoms in a harmonic trap We consider Nparticles in one dimension in an external potential, mw2 K(x) = 2 X7. (to)Write the complete Hamiltonian function for the system. Then calculate the number of micro-states MAND) by means of the semiclassical approach. (b)Calculate the entropy in the thermodynamic limit. (c)Calculate the temperature and the work differential based on the result in part (b).arrow_forward
- An ideal gas initially at P, V, and T, is taken through a cydle as shown below. (Let the factor n - 3.3.) P B P, V. (a) Find the net work done on the gas per cycle for 2.45 mol of gas initially at 0°C. kJ (b) What is the net energy added by heat to the system per cycle?arrow_forwardAt steady state, a thermodynamic cycle operating between hot and cold reservoirs at 1000 K and 500 K, respectively, receives energy by heat transfer from the hot reservoir at a rate of 1500 kW, discharges energy by heat transfer to the cold reservoir, and develops power at a rate of (a) 1000 kW, (b) 750 kW, (c) 0 kW. For each case, apply Eq. 5.13 on a time- rate basis to determine whether the cycle operates reversibly, operates irreversibly, or is impossible.arrow_forwardA plastic bag containing 0.2 kg of water at 20°C is dropped from a height of 0.5 m onto an insulating carpet. Assume that the bag does NOT break. What is the approximate probability that a similar bag sitting on a carpet will do the reverse; that is, spontaneously jump 0.5 m in the air? Express your answer in the form "Probability = 10-x," where x is a number you will calculate. (Hint: Note that ey = 10y÷ln(10).)arrow_forward
- The essential principle difference between the microcanonical and canonical Ensemble is that in the former the energy of the system is constant E, while in the latter the energy fluctuates in such a way that the value of the internal energy corresponding to the thermodynamic state of U = (E) the system is the expected value of its energy, Let us now examine this difference in the case of an ideal gas. Let the number of particles in the gas be N, the temperature T and the volume V. Determine the relative rms-value (root-mean-square) of the energy fluctuation for the gas. SErms U what is the magnitude of the fluctuations with the macroscopic number of particles? [((E – U)²)] ¹/² Uarrow_forwardStatistical Physics This is the chemical potential of an ideal gas. The second image is the answer to 4.20 problem. Please generate a solution for this problem (to validate the given answer). Thank you!arrow_forwardProve that entropy is a state function.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage LearningUniversity Physics (14th Edition)PhysicsISBN:9780133969290Author:Hugh D. Young, Roger A. FreedmanPublisher:PEARSONIntroduction 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 LearningLecture- Tutorials for Introductory AstronomyPhysicsISBN:9780321820464Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina BrissendenPublisher:Addison-WesleyCollege 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