An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Chapter 5.5, Problem 81P
To determine
The shift in the freezing temperature of a dilute solution.
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Chapter 5 Solutions
An Introduction to Thermal Physics
Ch. 5.1 - Prob. 1PCh. 5.1 - Consider the production of ammonia from nitrogen...Ch. 5.1 - Prob. 3PCh. 5.1 - Prob. 4PCh. 5.1 - Consider a fuel cell that uses methane (natural...Ch. 5.1 - Prob. 6PCh. 5.1 - The metabolism of a glucose molecule (see previous...Ch. 5.1 - Derive the thermodynamic identity for G (equation...Ch. 5.1 - Sketch a qualitatively accurate graph of G vs. T...Ch. 5.1 - Suppose you have a mole of water at 25C and...
Ch. 5.1 - Suppose that a hydrogen fuel cell, as described in...Ch. 5.1 - Prob. 12PCh. 5.1 - Prob. 13PCh. 5.1 - Prob. 14PCh. 5.1 - Prob. 15PCh. 5.1 - Prob. 16PCh. 5.1 - Prob. 17PCh. 5.2 - Prob. 18PCh. 5.2 - In the previous section 1 derived the formula...Ch. 5.2 - Prob. 20PCh. 5.2 - Is heat capacity (C) extensive or intensive? What...Ch. 5.2 - Prob. 22PCh. 5.2 - Prob. 23PCh. 5.3 - Go through the arithmetic to verify that diamond...Ch. 5.3 - Prob. 25PCh. 5.3 - How can diamond ever be more stable than graphite,...Ch. 5.3 - Prob. 27PCh. 5.3 - Calcium carbonate, CaCO3, has two common...Ch. 5.3 - Aluminum silicate, Al2SiO5, has three different...Ch. 5.3 - Sketch qualitatively accurate graphs of G vs. T...Ch. 5.3 - Sketch qualitatively accurate graphs of G vs. P...Ch. 5.3 - The density of ice is 917kg/m3. (a) Use the...Ch. 5.3 - An inventor proposes to make a heat engine using...Ch. 5.3 - Below 0.3 K the Slope of the 3He solid–liquid...Ch. 5.3 - Prob. 35PCh. 5.3 - Effect of altitude on boiling water. (a) Use the...Ch. 5.3 - Prob. 37PCh. 5.3 - Prob. 38PCh. 5.3 - Prob. 39PCh. 5.3 - The methods of this section can also be applied to...Ch. 5.3 - Suppose you have a liquid (say, water) in...Ch. 5.3 - Ordinarily, the partial pressure of water vapor in...Ch. 5.3 - Assume that the air you exhale is at 35C, with a...Ch. 5.3 - Prob. 44PCh. 5.3 - Prob. 46PCh. 5.3 - Prob. 47PCh. 5.3 - Prob. 48PCh. 5.3 - Prob. 49PCh. 5.3 - The compression factor of a fluid is defined as...Ch. 5.3 - Prob. 51PCh. 5.3 - Prob. 52PCh. 5.3 - Repeat the preceding problem for T/Tc=0.8.Ch. 5.3 - Prob. 54PCh. 5.3 - Prob. 55PCh. 5.4 - Prove that the entropy of mixing of an ideal...Ch. 5.4 - In this problem you will model the mixing energy...Ch. 5.4 - Suppose you cool a mixture of 50% nitrogen and 50%...Ch. 5.4 - Suppose you start with a liquid mixture of 60%...Ch. 5.4 - Suppose you need a tank of oxygen that is 95%...Ch. 5.4 - Prob. 62PCh. 5.4 - Everything in this section assumes that the total...Ch. 5.4 - Figure 5.32 shows the phase diagram of plagioclase...Ch. 5.4 - Prob. 65PCh. 5.4 - Prob. 66PCh. 5.4 - Prob. 67PCh. 5.4 - Plumbers solder is composed of 67% lead and 33%...Ch. 5.4 - What happens when you spread salt crystals over an...Ch. 5.4 - What happens when you add salt to the ice bath in...Ch. 5.4 - Figure 5.35 (left) shows the free energy curves at...Ch. 5.4 - Repeat the previous problem for the diagram in...Ch. 5.5 - If expression 5.68 is correct, it must be...Ch. 5.5 - Prob. 74PCh. 5.5 - Compare expression 5.68 for the Gibbs free energy...Ch. 5.5 - Seawater has a salinity of 3.5%, meaning that if...Ch. 5.5 - Osmotic pressure measurements can be used to...Ch. 5.5 - Because osmotic pressures can be quite large, you...Ch. 5.5 - Most pasta recipes instruct you to add a teaspoon...Ch. 5.5 - Use the Clausius–Clapeyron relation to derive...Ch. 5.5 - Prob. 81PCh. 5.5 - Use the result of the previous problem to...Ch. 5.6 - Prob. 83PCh. 5.6 - Prob. 84PCh. 5.6 - Prob. 85PCh. 5.6 - Prob. 86PCh. 5.6 - Sulfuric acid, H2SO4, readily dissociates into H+...Ch. 5.6 - Prob. 88PCh. 5.6 - Prob. 89PCh. 5.6 - When solid quartz dissolves in water, it combines...Ch. 5.6 - When carbon dioxide dissolves in water,...Ch. 5.6 - Prob. 92P
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- e. Consider one unit cell and assume the length of the side of the cube is “a”. Remember that “a” is the distance between the centers of two adjacent atoms. How long is “a”, the edge of a unit cell, in terms of radius, r, of an atom? Write also your answer in the summary table.Answer: __________f. Based on the earlier questions, a simple cubic cell has the equivalent of only 1 atom. Recall the volume of sphere with radius, r, is expressed as V = 4/3 πr3. With this information, find the total volume of all the spheres in this unit cell, expressed in terms of r. (Hint: To do this, take the total number of atoms and multiply it by the volume of one atom, with radius, r)Answer: __________arrow_forwardThe density of copper is 8.96 g/cm3 , and its atomic weight is 63.5 g/mole. Calculate the Fermi energy for copper (Equation 5.54). Assume d = 1, and give your answer in electron voltsarrow_forwardA sample of copper has a mass of 10.68 g when measured in air. It has a mass of 9.47 g when measured in water. Answer these three questions: How many atoms are in the sample? What is the simple volume of the space including and surrounding each atom? Assume the atoms are evenly distributed throughout the sample. That is no FCC, BCC, or HCP crystal structure. What is the diameter of each atom?arrow_forward
- The Clausius-Clapeyron relation 5.47 is a differential equation that can, in principle, be solved to find the shape of the entire phase-boundary curve. To solve it, however, you have to know how both L and ~V depend on temperature and pressure. Often, over a reasonably small section of the curve, you can take L to be constant. Moreover, if one of the phases is a gas, you can usually neglect the volume of the condensed phase and just take ~V to be the volume of the gas, expressed in terms of temperature and pressure using the ideal gas law. Making all these assumptions, solve the differential equation explicitly to obtain the following formula for the phase boundary curve:This result is called the vapor pressure equation. Caution: Be sure to use this formula only when all the assumptions just listed are valid.arrow_forwardA sample of copper has a mass of 10.68 g when measured in air. It has a mass of 9.47 g when measured in water. Answer these four questions: What is the density of the sample? How many atoms are in the sample? What is the simple volume of the space including and surrounding each atom? Assume the atoms are evenly distributed throughout the sample. That is no FCC, BCC, or HCP crystal structure. What is the diameter of each atom?arrow_forwardOne mole of silicon (6x1023 atoms) has a mass of 28 grams, as shown in the periodic table on the inside front cover of the textbook. The density of silicon is 2.4 grams/cm³. What is the approximate diameter of a silicon atom (length of a bond) in a solid block of the material? Make the simplifying assumption that the atoms are arranged in a "cubic" array, as shown in the figure. Remember to convert to SI units. d =arrow_forward
- Hi, could I get some help with this micro-macro connection physics problem involving the rotational frequency of a molecule? The set up is: Treating the diatomic oxygen molecule O2 as a perfect dumbbell with length 0.12 nm between the molecules, what is the rotational frequency of the molecule in gigahertz (GHz) at a cold temperature of 100 kelvin (K) to 4 digits of precision if kB = 1.38e-23 J/K and the mass of O2 is 16 u, where the atomic mass unit u = 1.66e-27 kg? Thank you.arrow_forwardSection 1.3 Space Lattices 1.1 Determine the number of atoms per unit cell in a (a) face-centered cubic, (b) body-centered cubic, and (c) diamond lattice.arrow_forwardHow do I solve 12.7? This problem is in a section called "Overview of Molecular Properties." The chapter is named Molecules. The portion that this problem is in is titled Systems With Two or More Atoms.arrow_forward
- With detailed solution please, thank you.arrow_forwardConsider air at P = 1.00 atm. The average molecular mass of air is approximately 29 u (atomic unit). Boltzmann constant is 1.380 × 10-23 J/K. What is the mass density in kg/m3 of air at T = -(2.75x10^1)°C? Use three significant digits for your answer. Note: Your answer is assumed to be reduced to the highest power possible. Your Answer: х10 Answerarrow_forwardThe vibrational frequency n for Br2 is 323 cm-1 and the energy difference between its two lowest rotational energy levels, J = 0 and J = 1, is 0.164 cm-1. Calculate the relative populations of the v = 1 and v = 0 vibrational energylevels and the relative populations of the two lowest rotational energy levels for Br2 at 300 K. Comment on your results.arrow_forward
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