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The First Law of Thermodynamics 167 at 300 K. Therefore, = = 5-57. In Chapter 8, we will derive the formula (8.22) Show that U is independent of volume for an ideal gas. Show that for an isothermal expansion of a van der Waals gas and that for a Redlich-Kwong gas. Using the equation PV = nRT, we have for an ideal gas. For the van der Waals equation, and For a Redlich-Kwong gas, and 5-58. Use the rigid rotator-harmonic oscillator model and the data in Table 4.2 to plot (T) for CO(g) from 300 K to 1000 K. Compare your result with the expression given in Problem 5-43.