Category: Schroeder’s TP Solutions

Problem 5.20 The first excited energy level of a hydrogen atom has an energy of 10.2 eV, if we take the ground-state energy to be zero. However, the first excited level is really four independent states, all with the same energy. We can therefore assign it an entropy of since for this given value of…

Problem 5.16 A formula analogous to that for relates the isothermal and isentropic compressibilities of a material: (Here is the reciprocal of the adiabatic bulk modulus considered in Problem 1.39.) Derive this formula. Also check that it is true for an ideal gas. Solution: Problem 5.16 Solution (Download)

Problem 5.14 The partial-derivative relations derived in Problems 1.46, 3.33, and 5.12, plus a bit more partial-derivative trickery, can be used to derive a completely general relation between and (a) With the heat capacity expressions from Problem 3.33 in mind, first consider to be a function of and Expand in terms of the partial derivatives…

Problem 5.12 Functions encountered in physics are generally well enough behaved that their mixed partial derivatives do not depend on which derivative is taken first. Therefore, for instance, where each is taken with fixed, each is taken with fixed, and is always held fixed. From the thermodynamic identity (for ) you can evaluate the partial…

Problem 5.6 A muscle can be thought of as a fuel cell, producing work from themetabolism of glucose: a) Use the data at the back of this book to determine the values of and for this reaction, for one mole of glucose. Assume that the reaction takes place at room temperature and atmospheric pressure. (b)…

Problem 5.4 In a hydrogen fuel cell, the steps of the chemical reaction are at – electrode: ;at + electrode: . Calculate the voltage of the cell. What is the minimum voltage required for electrolysis of water? Explain briefly Solution: Problem 5.4 Solution (Download)

Problem 5.2 Consider the production of ammonia from nitrogen and hydrogen, at 298 K and 1 bar. From the values of and tabulated at the back of this book, compute for this reaction and check that it is consistent with the value given in the table. Solution: Problem 5.2 Solution (Download)

Problem 5.1 Let the system be one mole of argon gas at room temperature and atmospheric pressure. Compute the total energy (kinetic only, neglecting atomic rest energies), entropy, enthalpy, Helmholtz free energy, and Gibbs free energy. Express all answers in SI units. Solution: Problem 5.1 Solution (Download)

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 , (b) Calculate the efficiency of…

Problem 3.35 In the text I showed that for an Einstein solid with three oscillators and three units of energy, the chemical potential is (where is the size of an energy unit and we treat each oscillator as a “particle”). Suppose instead that the solid has three oscillators and four units of energy. How does…