An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Chapter 5.6, Problem 89P
To determine
The equilibrium constant at
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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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- Recall Problem 1.34, which concerned an ideal diatomic gas taken around a rectangular cycle on a PV diagram. Suppose now that this system is used as a heat engine, to convert the heat added into mechanical work. (a) Evaluate the efficiency of this engine for the case V2 = 3V1 , P2 = 2P1. (b) Calculate the efficiency of an "ideal" engine operating between the same temperature extremes.arrow_forwardProblem 1.33. An ideal gas is made to undergo the cyclic process shown in Figure 1.10(a). For each of the steps A, B, and C, determine whether each of the following is positive, nogative, or zero: (a) the work done on the gas; (b) the change in the energy content of the gas: (c) the heat added to the gas. Then determine the sign of each of these three quantities for the whole cycle. What does this process accomplish? (a) A (b) B Pa B A A D Volume V1 V Volume Figure 1.10. PV diagrams for Problems 1.33 and 1.34. steps; for example, during step A, heat is added to the gas (from an external flame or something) while the piston is held fixed. (c) Compute the net work done on the gas, the net heat added to the gas, and the net change in the energy of the gas during the entire cycle. Are the results as you expected? Explain briefly. Show that knowing the initial condition of a compressed system consisting of a gas you can derive its final temperature. Pressure Pressurearrow_forwardrork 28 the ofnly Problem 1.31. Imagine some helium in a cylinder with an initial volume of 1 liter and an initial pressure of 1 atm. Somehow the helium is made to expand to a final volume of 3 liters, in such a way that its pressure rises in direct proportion to its volume. (a) Sketch a graph of pressure vs. volume for this process. (b) Calculate the work done on the gas during this process, assuming that there are no "other" types of work being done. (c) Calculate the change in the helium's energy content during this process. (d) Calculate the amount of heat added to or removed from the helium during this process. (e) Describe what you might do to cause the pressure to rise as the helium еxpands. Problem 1.33. An ideal gas is made to undergo the cyclic process shown in Figure 1.10(a). For each of the steps A, B, and C, determine whether each of the following is positive, nogative, or zero: (a) the work done on the gas; (b) the change in the energy content of the gas; (c) the heat…arrow_forward
- Problem 1.2. The Rankine temperature scale (abbreviated °R) uses the same size degrees as Fahrenheit, but measured up from absolute zero like kelvin (so Rankine is to Fahrenheit as kelvin is to Celsius). Find the conversion formula between Rankine and Fahrenheit, and also between Rankine and kelvin. What is room temperature on the Rankine scale?arrow_forwardProblem 6.33. Calculate the most probable speed, average speed, and rms speed for oxygen (O₂) molecules at room temperature.arrow_forwardThe 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_forward
- The carrier distributions in the conduction and valence bands were noted to peak at energies close to the band edges. (Refer to carrier distribution in Fig. 1-20.) Using Boltzmann approximation, show that the energy at which the carrier distribution peaks is Ec+kT/2 and E-kT/2 for the conduction and valence bands, respectively.arrow_forwardUse a computer to reproduce the table and graph in Figure 2.4: two Einstein solids, each containing three harmonic oscillators, with a total of six units of energy. Then modify the table and graph to show the case where one Einstein solid contains six harmonic oscillators and the other contains four harmonic oscillators (with the total number of energy units still equal to six). Assuming that all microstates are equally likely, what is the most probable macrostate, and what is its probability? What is the least probable macrostate, and what is its probability?arrow_forwardThe temperature (in °C)at time t (in hours) in an art museum varies according to the function T(t) = 20+5cos (0.262t). Set-up the integral that will give you the average temperature over the period [2, 6]. Produce the appropriate antiderivative. Once these two are calculated please use your calculator to approximate the average to the nearest tenth.arrow_forward
- 2.2 Consider a van der Waal's gas that undergoes an isothermal expansion from volume V₁ to volume V₂. (a) (b) Calculate the change in the Helmholtz free energy. From the theory of thermodynamics, with 7 and V p. Show that the change in independent, (a) T V (OV)₁ = 7 (SP), ), internal energy is AU = a a (1/17 - 12/2). G V₂arrow_forwardFor an Einstein solid with each of the following values of Nand q, list all of the possible microstates, count them, and verify formula 2.9. N = 4, q = 2arrow_forwardUse the Maxwell distribution to calculate the average value of v2 for the molecules in an ideal gas. Check that your answer agrees with equation 6.41 (Attached).arrow_forward
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