PHYSICS 425 & 625 Homework [example] [fortran on the mac] [return to main page]
Extra Credit: |
Homework 17 |
Homework 16 1. How is the Gibbs factor different from the Boltzmann factor? 2. Why is it that quantum statistics are different for particles called Bosons and Fermions? 3. What keeps matter from collapsing under the huge electrostatic forces that try to pull electrons and protons together? 4. What is the ultraviolet catastrophe? 5. How does the total energy density of a black body vary with temperature? Think about the Earth at a lowly 285 K, the Sun exterior at 5800 K, and the Sun interior at around 15 million K. 6. How does the entropy of a black body relate to the number of photons in a black body? 7. What is the value of the Stefan Boltzmann constant? Use it to estimate how much radiative power your body would emit (neglecting clothes). How many food calories would you need to eat to replace the energy you would lose in 12 hours due to black body radiation emission if you did not receive infrared energy from the environment. 8. How is the Debye theory of solids different from the Einstein theory of solids? 9. What is Bose Einstein condensation? |
Homework 15 |
Homework 14 (due date moved). OR
OR You can do both with one for extra credit. |
Homework 13 In 6.3 it is a good idea to plot the partition function as a function of (kT/epsilon) too so you can see the functional form. Boltzmann's constant is given in eV/K on page 402. On problem 6.10, you can calculate the partition function by adding terms, and can quit adding terms when they are so small that they don't contribute anymore. On problem 6.10, calculate the wavelength of a photon (in micron units) that corresponds to an excitation from the ground state to the first excited state; what part of the electromagnetic spectrum is this photon in? |
Homework 12 1. How is the Boltzmann factor defined. Why is it useful? 2. What does the partition function partition? 3. What assumption(s) must be made when deriving the equipartition theorem? 4. Sketch the Maxwell speed distribution. Why don't all molecules in an ideal gas just have the same average speed? 5. What is the relationship between the partition function and the Helmholtz free energy? |
Homework 11 |
Homework 10 |
Homework 9 1. What is temperature (refined answer from our chapter 1 definition)? 2. How do you calculate entropy from heat capacity? 3. What is the 'third law' and how does it affect entropy? 4. Do you agree with the author's silly economic/entropy analogy? 5. What are negative absolute temperatures? 6. What are the conditions for mechanical equilibrium in two systems? 7. What is diffusive equilibrium? 8. What is the chemical potential? 9. What are the conditions of diffusive equilibrium? 10. Write down equations for obtaining temperature, pressure, and chemical potential from partial derivatives of entropy. |
Homework 8 |
Homework 7 |
Homework 6 |
Homework 5 |
Homework 4 Turn in these questions for review: 1. What is a microstate? 2. What is a macrostate? 3. Write down the fundamental assumption of Statistical Mechanics. Do you agree with it? Explain. 4. What is the author's physical explanation of heat? Do you agree? 5. The author gives a statement of the second law of thermodynamics. Write it down. Do you agree with it? 6. What is the Stirling approximation? Why is it useful? 7. What is the thermodynamic limit? 8. Write down the fundamental equation for entropy and define all the terms. Discuss this definition. What do large values of entropy imply? Small values? 9. Give an example of a reversible and irreversible process. 10. Read problems 2.41, 2.42, and 2.43 carefully, and think about them. |
Homework 3
Mathematica code for the plot: Plot[Evaluate[ Table[Exp[-x^2/(4 t)]/Sqrt[t], {t, .25, 5, 0.25}]], {x, -10, 10}, PlotRange -> {{-10, 10}, {0, 2}}, AxesLabel -> {"x", "T(x)" - SubscriptBox[T, 0] // DisplayForm}, Frame -> False, BaseStyle -> {FontWeight -> "Bold", FontSize -> 14}] Code for the animation: Animate[Plot[Exp[-x^2/(4 t)]/Sqrt[t], {x, -10, 10}, Filling -> Axis, FillingStyle -> Red, PlotRange -> {{-10, 10}, {0, 2}}, AxesLabel -> {"x", "T(x)" - SubscriptBox[T, 0] // DisplayForm}, Frame -> False, BaseStyle -> {FontWeight -> "Bold", FontSize -> 14}], {t, 0.25, 5, 0.1}] Try with Mathematica Online. |
Homework 2 due Thursday 15 September QUESTIONS FOR REVIEW (copy and paste these to your word processor, answer them, and turn them in with the problems): Do problems: |
Homework 1 due Tuesday 6 September Temperature. QUESTIONS FOR REVIEW (copy and paste these to your word processor, answer them, and turn them in with the problems): a. What is temperature? Give three definitions. b. What is meant by thermal equilibrium? Can we do thermodynamics on systems that are not in thermal equilibrium? c. What are two mechanisms for objects to use to come to thermal equilibrium? d. In your experience, what is the relaxation time necessary for a hot cup of coffee, tea, or water to come to thermal equilibrium with at room at room temperature? e. What is the most exotic type of thermometer you can think of? f. What would you rather touch, a piece of fluffy carpet or a large piece of aluminum, if both are at 353 K? Why? PROBLEMS: On problem 1.7 you do not have to get a mercury thermometer. Just make an estimate of its size and design one to your liking. Comment on why might we not want to use mercury for a thermometer. Also, extra credit for a thorough discussion of why mercury is a liquid rather than solid at typical room conditions, in comparison with its nearest neighbors in the periodic table. |
Problems for homework and class discussion: 1.32, 1.34, 1.37, 1.40, 1.42, 1.43, 1.46, 1.47, 1.48, 1.50, 1.51, 1.54.
You can start thinking about them now.