Category: Schroeder’s TP Solutions

Problem 6.27 Use a computer to sum the exact rotational partition function (equation 6.30) numerically, and plot the result as a function of Keep enough terms in the sum to be confident that the series has converged. Show that the approximation in equation 6.31 is a bit low, and estimate by how much. Explain the…

Problem 6.24 For an molecule, the constant is approximately 0.00018 eV. Estimate the rotational partition function for an molecule at room temperature. Solution: Problem 6.24 Solution (Download)

Problem 6.23 For a CO molecule, the constant is approximately 0.00024 eV. (This number is measured using microwave spectroscopy, that is, by measuring the microwave frequencies needed to excite the molecules into higher rotational states.) Calculate the rotational partition function for a molecule at room temperature (300 K), first using the exact formula 6.30 and…

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…