Introduction To Quantum Mechanics
3rd Edition
ISBN: 9781107189638
Author: Griffiths, David J., Schroeter, Darrell F.
Publisher: Cambridge University Press
expand_more
expand_more
format_list_bulleted
Question
Chapter 11.5, Problem 11.21P
To determine
Berry’s phase for one cycle of the process in Example 11.4.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
A rigid container contains a mixture of 2mols of a polyatomic gas at a temperature of 3000K. You then heat the mixture providing 39907.02J of heat. At the end of the process, the mixture is at a temperature of 3600K.If at 3000K the translational as well as the 3 rotational degrees of freedom of the polyatomic gas are already activated, how many vibrational degrees of freedom does it have activated in this temperature range? (Assume the number of degrees of freedom does not change during the process).
Soru
What is the formula for the fluctuation in the (internal) energy of a system
Ou? Prove by direct aifferentiation and using
a(log Z)|
U = k T².
ƏT
that the fluctuation in the energy is given by the following formula:
听=kgT2
Ine
%3D
V.N
Gibb’s free energy is defined as G≡H-TS and H ≡ U+PV. Show that dU=TdS-PdV, dH=TdS+VdP and dG=VdP-SdT.
2. If non-PV work is done (P and T constant), dU= TdS-PdV +dwother. Knowing that dH=dU+PdV+VdP and dG= dH-SdT-TdS, show that dG=dwother. We often call free energy the chemical work for a reaction!
Chapter 11 Solutions
Introduction To Quantum Mechanics
Ch. 11.1 - Prob. 11.1PCh. 11.1 - Prob. 11.2PCh. 11.1 - Prob. 11.3PCh. 11.1 - Prob. 11.4PCh. 11.1 - Prob. 11.5PCh. 11.1 - Prob. 11.6PCh. 11.1 - Prob. 11.7PCh. 11.1 - Prob. 11.8PCh. 11.1 - Prob. 11.9PCh. 11.3 - Prob. 11.10P
Ch. 11.3 - Prob. 11.11PCh. 11.3 - Prob. 11.12PCh. 11.3 - Prob. 11.13PCh. 11.3 - Prob. 11.14PCh. 11.3 - Prob. 11.15PCh. 11.3 - Prob. 11.16PCh. 11.4 - Prob. 11.17PCh. 11.5 - Prob. 11.18PCh. 11.5 - Prob. 11.19PCh. 11.5 - Prob. 11.20PCh. 11.5 - Prob. 11.21PCh. 11.5 - Prob. 11.22PCh. 11 - Prob. 11.23PCh. 11 - Prob. 11.24PCh. 11 - Prob. 11.25PCh. 11 - Prob. 11.26PCh. 11 - Prob. 11.27PCh. 11 - Prob. 11.28PCh. 11 - Prob. 11.29PCh. 11 - Prob. 11.30PCh. 11 - Prob. 11.31PCh. 11 - Prob. 11.33PCh. 11 - Prob. 11.35PCh. 11 - Prob. 11.36PCh. 11 - Prob. 11.37P
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
- What is the formula for the fluctuation in the (internal) energy of a system Oy? Prove by direct differentiation and using Ə (log Z)| U = kgT² ƏT that the fluctuation in the energy is given by the following formula: of = kgT². ƏT V,Narrow_forward7.6 The sketch shows a common consumer product called the Water Pik. This device uses a motor to drive a piston pump that produces a jet of water (d = 3 mm, T = 10°C) with a speed of 25 m/s. Estimate the minimum electrical power in watts that is required by the device. Hints: (a) Assume that the power is used only to produce the kinetic energy of the water in the jet; and (b) in a time interval At, the amount of mass that flows out the nozzle is Am, and the corresponding amount of ki- netic energy is (AmV²/2). Water reservoir High-speed water jet Motor and pump сеее PROBLEM 7.6arrow_forwardSketch a qualitatively accurate graph of G vs. T for a pure substance as it changes from solid to liquid to gas at fixed pressure. Think carefully about the slope of the graph. Mark the points of the phase transformations and discuss the features of the graph briefly.arrow_forward
- ANSWER THE FOLLOWING QUESTIONS: 1. Why is it impossible for a totally isolated system to exist in nature? Explain briefly. 2. What is the sum of the kinetic and potential energy of a system? 3. The living cell exhibits thermodynamic equilibrium. True or False? Why?arrow_forwardTwo rods have the same size in dimeter А and both made of the same material. The system is released when 0=0° . L, L1+L2=L , determine L1/L2 such that A will reach the maximum speed when 1 L2 O=90°. Find the referring speed of A. Barrow_forwardA rigid container contains a mixture of 2 moles of a monoatomic gas with 1 mol of a polyatomic gas at a temperature of 3000 K. You then heat the mixture by supplying 39907.2 J of heat. At the end of the process, the mixture is at a temperature of 3600 K. If at 3000 K the translational as well as the 3 rotational degrees of freedom of the polyatomic gas are already activated, how many vibrational degrees of freedom does it have activated in this temperature range? (assume that the number of degrees of freedom does not change during the process) If necessary, consider: R = 8.314 J/mol∙K1 cal = 4.19 Jkb =1,38 x 10⁻²³ m² kg s⁻² K⁻¹arrow_forward
- The only form of energy possessed by molecules of a monatomic ideal gas is translational kinetic energy. Using the results from the discussion of kinetic theory in Section 10.5, show that the internal energy of a monatomic ideal gas at pressure P and occupying volume V may be written as U = 3/2PVarrow_forwardStarting with an ideal gas particle bouncing around in a cube, derive the relationship between the energy and the pressure and volume. Use the ideal gas law to relate kinetic energy and temperature.arrow_forwardCharacterize the paths as shown as isobaric, isovolumetric, isothermal, or adiabatic. For path B, Q = 0. The blue curves are isotherms.arrow_forward
- Use the Gibbs expression for entropy (eqn 14.48) to derive the formula for the entropy of mixing (eqn 14.40). Below are equations 14.48 and 14.40 - AS-NkB(x ln x + (1 − x) ln(1 - x)). = S = -kB Piln P¿. (14.40) (14.48)arrow_forwardA PV module produces a nominal 340 W and the dimensions are 1.521 m X 1.116 m. What is the module power density? The owner wants to have at least a 5 kW system using this module. Assuming nominal power production, how many modules would be needed to produce at least 5 kW (assume two equal length rows)? What would be the final surface area and nominal power output of the array?arrow_forwardConsider 1.5 mol of pure nitrogen gas N2 which we will treat as a diatomic ideal gas. From 100 K to 1000 K, the gas has three translational and two rotational degrees of freedom. Above 1000 K, there are two additional vibrational degrees of freedom. The molar mass of N2 is 0.028 kg/mol. a. If the nitrogen molecules have an rms translational molecular speed of 511 m/s, what is the temperature of the gas? b. What is the internal energy U of the nitrogen gas at the temperature from part a? c. If the nitrogen gas has a pressure of 1.2 atm, what volume (in liters) does it occupy at the temperature from part a? d How much heat would be required to raise the temperature of the gas from 1500 K to 1800 K, at a constant volume? Remember that vibrational degrees of freedom are active at these temperatures.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
The Laws of Thermodynamics, Entropy, and Gibbs Free Energy; Author: Professor Dave Explains;https://www.youtube.com/watch?v=8N1BxHgsoOw;License: Standard YouTube License, CC-BY