Author: Tru Physics

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…

Problem 2.23 Consider a two-state paramagnet with elementary dipoles, with the total energy fixed at zero so that exactly half the dipoles point up and half point down.(a) How many microstates are “accessible” to this system?(b) Suppose that the microstate of this system changes a billion times per second. How many microstates will it explore…

Problem 2.22 This problem gives an alternative approach to estimating the width of the peak of the multiplicity function for a system of two large Einstein solids. (a) Consider two identical Einstein solids, each with N oscillators, in thermal contact with each other. Suppose that the total number of energy units in the combined system…

Problem 2.16 Suppose you flip 1000 coins. (a) What is the probability of getting exactly 500 heads and 500 tails? (Hint: First write down a formula for the total number of possible outcomes. Then, to determine the “multiplicity” of the 500-500 “macrostate,” use Stirling’s approximation. If you have a fancy calculator that makes Stirling’s approximation…