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Chapter 5: Q.5.80 (page 208)
Use the Clausius-Clapeyron relation to derive equation 5.90 directly from Raoult's law. Be sure to explain the logic carefully.
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Repeat the preceding problem with T/TC=0.8
Consider a completely miscible two-component system whose overall composition is x, at a temperature where liquid and gas phases coexist. The composition of the gas phase at this temperature is and the composition of the liquid phase is . Prove the lever rule, which says that the proportion of liquid to gas is . Interpret this rule graphically on a phase diagram.
Effect of altitude on boiling water.
(a) Use the result of the previous problem and the data in Figure 5.11 to plot a graph of the vapor pressure of water between and . How well can you match the data at the two endpoints?
(b) Reading the graph backward, estimate the boiling temperature of water at each of the locations for which you determined the pressure in Problem 1.16. Explain why it takes longer to cook noodles when you're camping in the mountains.
(c) Show that the dependence of boiling temperature on altitude is very nearly (though not exactly) a linear function, and calculate the slope in degrees Celsius per thousand feet (or in degrees Celsius per kilometer).
Ordinarily, the partial pressure of water vapour in the air is less than the equilibrium vapour pressure at the ambient temperature; this is why a cup of water will spontaneously evaporate. The ratio of the partial pressure of water vapour to the equilibrium vapour pressure is called the relative humidity. When the relative humidity is 100%, so that water vapour in the atmosphere would be in diffusive equilibrium with a cup of liquid water, we say that the air is saturated. The dew point is the temperature at which the relative humidity would be 100%, for a given partial pressure of water vapour.
(a) Use the vapour pressure equation (Problem 5.35) and the data in Figure 5.11 to plot a graph of the vapour pressure of water from 0°C to 40°C. Notice that the vapour pressure approximately doubles for every 10° increase in temperature.
(b) Suppose that the temperature on a certain summer day is 30° C. What is the dew point if the relative humidity is 90%? What if the relative humidity is 40%?
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.
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