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Chapter 5: Q 5.63 (page 195)
Everything in this section assumes that the total pressure of the system is fixed. How would you expect the nitrogen-oxygen phase diagram to change if you increase or decrease the pressure? Justify your answer.
The phase area will get smaller.
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Let the system be one mole of argon gas at room temperature and atmospheric pressure. Compute the total energy (kinetic only, neglecting atomic rest energies), entropy, enthalpy, Helmholtz free energy, and Gibbs free energy. Express all answers in SI units.
Check that equations 5.69 and 5.70 satisfy the identity (equation 5.37)
In this problem you will derive approximate formulas for the shapes of the phase boundary curves in diagrams such as Figures 5.31 and 5.32, assuming that both phases behave as ideal mixtures. For definiteness, suppose that the phases are liquid and gas.
(a) Show that in an ideal mixture of A and B, the chemical potential of species A can be written where A is the chemical potential of pure A (at the same temperature and pressure) and . Derive a similar formula for the chemical potential of species B. Note that both formulas can be written for either the liquid phase or the gas phase.
(b) At any given temperature T, let x1 and xgbe the compositions of the liquid and gas phases that are in equilibrium with each other. By setting the appropriate chemical potentials equal to each other, show that x1and xg obey the equations = and where represents the change in G for the pure substance undergoing the phase change at temperature T.
(c) Over a limited range of temperatures, we can often assume that the main temperature dependence of comes from the explicit T; both are approximately constant. With this simplification, rewrite the results of part (b) entirely in terms of TA, and TB (eliminating ). Solve for x1and xgas functions of T.
(d) Plot your results for the nitrogen-oxygen system. The latent heats of the pure substances are. Compare to the experimental diagram, Figure 5.31.
(e) Show that you can account for the shape of Figure 5.32 with suitably chosen values. What are those values?
What happens when you spread salt crystals over an icy sidewalk? Why is this procedure rarely used in very cold climates?
Suppose that an unsaturated air mass is rising and cooling at the dry adiabatic lapse rate found in problem 1.40. If the temperature at ground level is 25 C and the relative humidity there is 50%, at what altitude will this air mass become saturated so that condensation begins and a cloud forms (see Figure 5.18)? (Refer to the vapor pressure graph drawn in Problem 5.42)
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