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Chapter 12: Problem 10
Why does your bathroom mirror often fog up when you shower?
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On entering a dwelling maintained at \(20^{\circ} \mathrm{C}\) from the outdoors where the temperature is \(10^{\circ} \mathrm{C}\), a person's eye-glasses are observed not to become fogged. A humidity gauge indicates that the relative humidity in the dwelling is \(55 \%\). Can this reading be correct? Provide supporting calculations.
A system consists initially of \(n_{\mathrm{A}}\) moles of gas \(\mathrm{A}\) at pressure \(p\) and temperature \(T\) and \(n_{\mathrm{B}}\) moles of gas B separate from gas A but at the same pressure and temperature. The gases are allowed to mix with no heat or work interactions with the surroundings. The final equilibrium pressure and temperature are \(p\) and \(T\), respectively, and the mixing occurs with no change in total volume. (a) Assuming ideal gas behavior, obtain an expression for the entropy produced in terms of \(\bar{R}, n_{\mathrm{A}}\), and \(n_{\mathrm{B}}\) (b) Using the result of part (a), demonstrate that the entropy produced has a positive value. (c) Would entropy be produced when samples of the same gas at the same temperature and pressure mix? Explain.
Air at \(30^{\circ} \mathrm{C}, 1\) bar, \(50 \%\) relative humidity enters an insulated chamber operating at steady state with a mass flow rate of \(3 \mathrm{~kg} / \mathrm{min}\) and mixes with a saturated moist air stream entering at \(5^{\circ} \mathrm{C}, 1\) bar with a mass flow rate of \(5 \mathrm{~kg} / \mathrm{min}\). A single mixed stream exits at 1 bar. Determine (a) the relative humidity and temperature, in \({ }^{\circ} \mathrm{C}\), of the exiting stream. (b) the rate of exergy destruction, in \(\mathrm{kW}\), for \(T_{0}=20^{\circ} \mathrm{C}\). Neglect kinetic and potential energy effects.
Helium at \(400 \mathrm{~K}, 1\) bar enters an insulated mixing chamber operating at steady state, where it mixes with argon entering at \(300 \mathrm{~K}, 1\) bar. The mixture exits at a pressure of \(1 \mathrm{bar}\). If the argon mass flow rate is \(x\) times that of helium, plot versus \(x\) (a) the exit temperature, in \(\mathrm{K}\). (b) the rate of exergy destruction within the chamber, in \(\mathrm{kJ}\) per \(\mathrm{kg}\) of helium entering. Kinetic and potential energy effects can be ignored. Let \(T_{0}=\) \(300 \mathrm{~K}\).
A stream consisting of \(35 \mathrm{~m}^{3} / \mathrm{min}\) of moist air at \(14^{\circ} \mathrm{C}\), \(1 \mathrm{~atm}, 80 \%\) relative humidity mixes adiabatically with a stream consisting of \(80 \mathrm{~m}^{3} / \mathrm{min}\) of moist air at \(40^{\circ} \mathrm{C}, 1 \mathrm{~atm}\), \(40 \%\) relative humidity, giving a single mixed stream at \(1 \mathrm{~atm}\). Using the psychrometric chart together with the procedure of Prob. 12.58, determine the relative humidity and temperature, in \({ }^{\circ} \mathrm{C}\), of the exiting stream.
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