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 7.5, Problem 62P
To determine
To solve the integral and obtain the heat capacity. Solve the heat capacity at
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
9.1. 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).
x
Let 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.
Find q, △U, and the work done for path ACB for the mono atomic ideal gas system.
Chapter 7 Solutions
An Introduction to Thermal Physics
Ch. 7.1 - Prob. 1PCh. 7.1 - Prob. 3PCh. 7.1 - Prob. 4PCh. 7.1 - Show that when a system is in thermal and...Ch. 7.1 - Prob. 7PCh. 7.2 - Prob. 8PCh. 7.2 - Prob. 9PCh. 7.2 - Prob. 11PCh. 7.2 - Prob. 12PCh. 7.2 - Prob. 13P
Ch. 7.2 - Prob. 14PCh. 7.2 - Prob. 15PCh. 7.2 - Prob. 16PCh. 7.2 - Prob. 17PCh. 7.2 - Prob. 18PCh. 7.3 - Prob. 19PCh. 7.3 - Prob. 20PCh. 7.3 - Prob. 21PCh. 7.3 - Prob. 22PCh. 7.3 - Prob. 24PCh. 7.3 - Prob. 25PCh. 7.3 - Prob. 26PCh. 7.3 - Prob. 29PCh. 7.3 - Prob. 32PCh. 7.3 - Prob. 33PCh. 7.3 - Prob. 34PCh. 7.4 - Prob. 37PCh. 7.4 - Prob. 38PCh. 7.4 - Prob. 39PCh. 7.4 - Prob. 40PCh. 7.4 - Prob. 41PCh. 7.4 - Prob. 42PCh. 7.4 - Prob. 43PCh. 7.4 - Prob. 44PCh. 7.4 - Prob. 45PCh. 7.4 - Prob. 46PCh. 7.4 - Prob. 47PCh. 7.4 - Prob. 48PCh. 7.4 - Prob. 49PCh. 7.4 - Prob. 50PCh. 7.4 - Prob. 51PCh. 7.4 - Prob. 52PCh. 7.4 - Prob. 53PCh. 7.4 - Prob. 54PCh. 7.4 - Prob. 55PCh. 7.4 - Prob. 56PCh. 7.5 - Prob. 57PCh. 7.5 - Prob. 58PCh. 7.5 - Prob. 59PCh. 7.5 - Prob. 60PCh. 7.5 - The heat capacity of liquid 4He below 0.6 K is...Ch. 7.5 - Prob. 62PCh. 7.5 - Prob. 63PCh. 7.5 - Prob. 64PCh. 7.6 - Prob. 65PCh. 7.6 - Prob. 66PCh. 7.6 - Prob. 67PCh. 7.6 - Prob. 68PCh. 7.6 - If you have a computer system that can do...Ch. 7.6 - Prob. 70PCh. 7.6 - Prob. 71PCh. 7.6 - Prob. 72PCh. 7.6 - Prob. 73PCh. 7.6 - Prob. 75P
Knowledge Booster
Similar questions
- ANSWER PROBLEM 7.28 7.28. For the window in Problem 7.27, Calculate the transmitted and absorbed solar heat gain, using the detailed approach.arrow_forwardThe intensities of spectroscopic transitions between the vibrational states of a molecule are proportional to the square of the integral ∫ψv′xψvdx over all space. Use the relations between Hermite polynomials given in Table 7E.1 to show that the only permitted transitions are those for which v′ = v ± 1 and evaluate the integral in these cases.arrow_forwardThe 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.arrow_forward
- Check my work The highway fuel economy of a 2016 Lexus RX 350 FWD 6-cylinder 3.5-L automatic 5-speed using premium fuel is a normally distributed random variable with a mean of u = 2050 mpg and a standard deviation of o = 3.00 Ompg. (a) What is the standard error of X , the mean from a random sample of 36 fill-ups by one driver? (Round your answer to 4 decimal places.) Standard error of X (b) Within what interval would you expect the places.) nean to fall, with 99 percent probability? (Round your answers to 4 decimal The interval is from toarrow_forwardObtain relations for the characteristic lengths of a large plane wall of thickness 2L, a very long cylinder of radius ro, and a sphere of radius ro.arrow_forwardAssuming a source free region, derive the following equation. The symbols have the usual meaning. atarrow_forward
- Consider N identical harmonic oscillators (as in the Einstein floor). Permissible Energies of each oscillator (E = n h f (n = 0, 1, 2 ...)) 0, hf, 2hf and so on. A) Calculating the selection function of a single harmonic oscillator. What is the division of N oscillators? B) Obtain the average energy of N oscillators at temperature T from the partition function. C) Calculate this capacity and T-> 0 and At T-> infinity limits, what will the heat capacity be? Are these results consistent with the experiment? Why? What is the correct theory about this? D) Find the Helmholtz free energy from this system. E) Derive the expression that gives the entropy of this system for the temperature.arrow_forwardIf the given Vander Waals equation is (P+a/V^2)(V-b)=RT. The given states that a=3.592,R=0.08,b=0.04267, and P=10 and T=320. For finding V use a four step iteration.arrow_forwardProblem 1: This problem concerns a collection of N identical harmonic oscillators (perhaps an Einstein solid) at temperature T. The allowed energies of each oscillator are 0, hf, 2hf, and so on. a) Prove =1+x + x² + x³ + .... Ignore Schroeder's comment about proving 1-x the formula by long division. Prove it by first multiplying both sides of the equation by (1 – x), and then thinking about the right-hand side of the resulting expression. b) Evaluate the partition function for a single harmonic oscillator. Use the result of (a) to simplify your answer as much as possible. c) Use E = - дz to find an expression for the average energy of a single oscillator. z aB Simplify as much as possible. d) What is the total energy of the system of N oscillators at temperature T?arrow_forward
- 10.3. From the differential equation for the thermodynamic potential A(T, V), derive expressions for pressure P, entropy S, internal energy U, heat capacity at constant volume Cy, heat capacity at constant pressure Cp, volume expansivity B, and iso- thermal compressibility K.arrow_forwardConsider 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_forwardQ.2: A 5 mA diode is connected in series with a 100 ohms resistance and a DC voltage source derived from the output of a half-wave rectifier (HWR). The ac voltage driving the rectifier is of amplitude 35 volts. (a) What will be the DC current through the diode (use exponential l-V relation for the diode, and iteration method)? (b) What will be the ac resistance of the diode?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