602 The Kinetic Theory of GasesQ21.10The dry air is more dense. Since the air and the water vapor are at the same temperature, they havethe same kinetic energy per molecule. For a controlled experiment, the humid and dry air are at thesame pressure, so the number of molecules per unit volume must be the same for both. The watermolecule has a smaller molecular mass (18.0 u) than any of the gases that make up the air, so thehumid air must have the smaller mass per unit volume.Q21.11Suppose the balloon rises into air uniform in temperature. The air cannot be uniform in pressurebecause the lower layers support the weight of all the air above them. The rubber in a typical balloonis easy to stretch and stretches or contracts until interior and exterior pressures are nearly equal. Soas the balloon rises it expands. This is an isothermal expansion, with Pdecreasing as Vincreases bythe same factor in PVnRT=. If the rubber wall is very strong it will eventually contain the helium athigher pressure than the air outside but at the same density, so that the balloon will stop rising.
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This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .