Chapter 12: Problem 10
Why does your bathroom mirror often fog up when you shower?
Short Answer
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Chapter 12: Problem 10
Why does your bathroom mirror often fog up when you shower?
These are the key concepts you need to understand to accurately answer the question.
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Get started for freeA 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.
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 \(35^{\circ} \mathrm{C}, 3\) bar, \(30 \%\) relative humidity, and a velocity of \(50 \mathrm{~m} / \mathrm{s}\) expands isentropically through a nozzle. Determine the lowest exit pressure, in bar, that can be attained without condensation. For this exit pressure, determine the exit velocity, in \(\mathrm{m} / \mathrm{s}\). The nozzle operates at steady state and without significant potential energy effects.
Air at \(77^{\circ} \mathrm{C}, 1\) bar, and a molar flow rate of \(0.1 \mathrm{kmol} / \mathrm{s}\) enters an insulated mixing chamber operating at steady state and mixes with water vapor entering at \(277^{\circ} \mathrm{C}, 1\) bar, and a molar flow rate of \(0.3 \mathrm{kmol} / \mathrm{s}\). The mixture exits at 1 bar. Kinetic and potential energy effects can be ignored. For the chamber, determine (a) the temperature of the exiting mixture, in \({ }^{\circ} \mathrm{C}\). (b) the rate of entropy production, in \(\mathrm{kW} / \mathrm{K}\).
Answer the following questions involving a mixture of two gases: (a) When would the analysis of the mixture in terms of mass fractions be identical to the analysis in terms of mole fractions? (b) When would the apparent molecular weight of the mixture equal the average of the molecular weights of the two gases?
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