Tag: Schroeder's Introduction to Thermal Physics

Problem 3.5 Starting with the result of Problem 2.17, find a formula for the temperature of an Einstein solid in the limit Solve for the energy as a function of temperature to obtain (where is the size of an energy unit). Solution: Problem 3.5 Solution (Download)

Problem 3.1 Use Table 3.1 to compute the temperatures of solid and solid when Then compute both temperatures when Express your answers in terms of and then in kelvins assuming that Solution: Problem 3.1 Solution (Download)

Problem 2.39 Compute the entropy of a mole of helium at room temperature and atmospheric pressure, pretending that all the atoms are distinguishable. Compare to the actual entropy, for indistinguishable atoms, computed in the text. Solution: Problem 2.39 Solution (Download)

Problem 2.37 Using the same method as in the text, calculate the entropy of mixing for a system of two monatomic ideal gases, and , whose relative proportion is arbitrary. Let be the total number of molecules and let be the fraction of these that are of species . You should find Check that this…

Problem 2.34 Show that during the quasistatic isothermal expansion of a monatomic ideal gas, the change in entropy is related to the heat input by the simple formula In the following chapter I’ll prove that this formula is valid for any quasistaticprocess. Show, however, that it is not valid for the free expansion process described…

Problem 2.33 Use the Sackur-Tetrode equation to calculate the entropy of a mole of argon gas at room temperature and atmospheric pressure. Why is the entropy greater than that of a mole of helium under the same conditions? Solution: Problem 2.33 Solution (Download)

Problem 2.30 Consider again the system of two large, identical Einstein solidstreated in Problem 2.22. (a) For the case , compute the entropy of this system (in terms of Boltzmann’s constant), assuming that all of the microstates are allowed. (This is the system’s entropy over long time scales.)(b) Compute the entropy again, assuming that the…

Problem 2.29 Consider a system of two Einstein solids, with , , and (as discussed in Section 2.3). Compute the entropy of the most likely macrostate and of the least likely macrostate. Also compute the entropy over long time scales, assuming that all microstates are accessible. (Neglect the factor of Boltzmann’s constant in the definition…

Problem 2.28 How many possible arrangements are there for a deck of 52 playing cards? (For simplicity, consider only the order of the cards, not whether they are turned upside-down, etc.) Suppose you start with a sorted deck and shuffe it repeatedly, so that all arrangements become “accessible.” How much entropy do you create in…

Problem 2.27 Rather than insisting that all the molecules be in the left half of a container, suppose we only require that they be in the leftmost 99% (leaving the remaining 1% completely empty). What is the probability of finding such an arrangement if there are 100 molecules in the container? What if there are…