An Introduction to Thermal Physics
1st Edition
ISBN: 9780201380279
Author: Daniel V. Schroeder
Publisher: Addison Wesley
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Chapter 5.4, Problem 66P
To determine
The variation of the phase diagram for a system having a substantial negative mixing energy so that its free energy curve dips below the gas’s free energy curve.
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Under what conditions is the ideal-gas assumption suitable for real gases?
In this problem you are to consider an adiabaticexpansion of an ideal diatomic gas, which means that the gas expands with no addition or subtraction of heat.
Assume that the gas is initially at pressure p0, volume V0, and temperature T0. In addition, assume that the temperature of the gas is such that you can neglect vibrational degrees of freedom. Thus, the ratio of heat capacities is γ=Cp/CV=7/5.
Note that, unless explicitly stated, the variable γshould not appear in your answers--if needed use the fact that γ=7/5 for an ideal diatomic gas.
Find an analytic expression for p(V), the pressure as a function of volume, during the adiabatic expansion.
Express the pressure in terms of V and any or all of the given initial values p0, T0, and V0.
p(V) = __________
In this problem you are to consider an adiabaticexpansion of an ideal diatomic gas, which means that the gas expands with no addition or subtraction of heat.
Assume that the gas is initially at pressure p0, volume V0, and temperature T0. In addition, assume that the temperature of the gas is such that you can neglect vibrational degrees of freedom. Thus, the ratio of heat capacities is γ=Cp/CV=7/5.
Note that, unless explicitly stated, the variable γshould not appear in your answers--if needed use the fact that γ=7/5 for an ideal diatomic gas.
A) Find an analytic expression for p(V), the pressure as a function of volume, during the adiabatic expansion.
Express the pressure in terms of V and any or all of the given initial values p0, T0, and V0.
p(V) = __________
B) At the end of the adiabatic expansion, the gas fills a new volume V1, where V1>V0. Find W, the work done by the gas on the container during the expansion.
Express the work in terms of p0, V0, and V1. Your…
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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