Author: Tru Physics

Problem 6.9 In the numerical example in the text, I calculated only the ratio of the probabilities of a hydrogen atom being in two different states. At such a low temperature the absolute probability of being in a first excited state is essentially the same as the relative probability compared to the ground state. Proving…

Problem 6.5 Imagine a particle that can be in only three states, with energies -0.05 eV, 0, and 0.05 eV. This particle is in equilibrium with a reservoir at 300 K. (a) Calculate the partition function for this particle.(b) Calculate the probability for this particle to be in each of the three states.(c) Because the…

Problem 6.3 Consider a hypothetical atom that has just two states: a ground state with energy zero and an excited state with energy 2 eV. Draw a graph of the partition function for this system as a function of temperature, and evaluate the partition function numerically at T = 300 K, 3000 K, 30,000 K,…

Problem 6.2 Prove that the probability of finding an atom in any particular energy level is where and the “entropy” of a level is times the logarithm of the number of degenerate states for that level. Solution: Problem 6.2 Solution (Download)

Problem 5.82 Use the result of the previous problem to calculate the freezing temperature of seawater. Solution: Problem 5.82 Solution (Download)

Problem 5.81 Derive a formula, similar to equation 5.90, for the shift in the freezing temperature of a dilute solution. Assume that the solid phase is pure solvent, no solute. You should find that the shift is negative: The freezing temperature of a solution is less than that of the pure solvent. Explain in general…

Problem 5.76 Seawater has a salinity of 3.5%, meaning that if you boil away a kilogram of seawater, when you’re finished you’ll have 35 g of solids (mostly NaCl) left in the pot. When dissolved, sodium chloride dissociates into separate and ions. (a) Calculate the osmotic pressure difference between seawater and fresh water. Assume for…

Problem 5.57 Consider an ideal mixture of just 100 molecules, varying in composition from pure A to pure B. Use a computer to calculate the mixing entropy as a function of and plot this function (in units of ). Suppose you start with all A and then convert one molecule to type B; by how…

Problem 5.56 Prove that the entropy of mixing of an ideal mixture has an infinite slope, when plotted vs. , at and Solution: Problem 5.56 Solution (Download)

Problem 5.51 When plotting graphs and performing numerical calculations, it is convenient to work in terms of reduced variables, , , Rewrite the van der Waals equation in terms of these variables, and notice that the constants and disappear. Solution: Problem 5.51 Solution (Download)