PS4_2011

# PS4_2011 - Name Section Rec TA Side 1 of 4 Ch 1b Problem...

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Name Ch 1b, Problem Set Four Section Side 1 of 4 Due Friday, Jan. 28, 2011 Rec TA at 4 PM in the Drop Box 1. van der Waals Parameters (15 points) Recall van der Waals equation of state for gases, ቆܲ + ܽ ݊ ܸ ( ܸ െ ܾ݊ ) = ܴ݊ܶ where ܲ is pressure, ܸ is volume, ݊ is the number of moles, ܶ is absolute temperature, ܴ is the gas constant, and ܽ and ܾ are parameters. You’ll sometimes find tables that list values for van der Waals constants (for example: OGN, p. 118; lecture notes – pg. 2 of lecture 7), but what happens if you need these values for a gas that isn’t listed? You can always do experiments, but that’s usually quite difficult. In this problem you will find relationships between the van der Waals parameters and the critical properties of a substance. The critical temperature, ܶ , is the temperature above which the vapor of a substance cannot be liquefied. The critical pressure, ܲ , is the pressure required to liquefy the gas at the critical temperature. The critical volume, ܸ , is the volume of a fixed mass of fluid at critical temperature and pressure. You’re much more likely to find a table of critical values than van der Waals parameters. (a) Express van der Waals equation in terms of the specific molar volume ܸ , where ܸ = ܸ ݊ Τ . ( 2 points ) (b) Experimental data on all real substances at their critical temperature indicates that the ܲ െ ܸ isotherm passes through a horizontal inflection point at the critical pressure of a substance. Mathematically, this statement means ߲ܲ ߲ܸ = ߲ ܲ ߲ܸ = 0 when ܲ = ܲ and ܶ = ܶ Use this mathematical relationship to express the van der Waals constants ܽ and ܾ in terms of critical properties. Since tables usually only report critical temperatures and pressures, you should express your answer so that only ܴ , ܶ and ܲ appear. ( 13 points )

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Name Ch 1b, Problem Set Four Section Side 2 of 4 Due Friday, Jan. 28, 2011
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PS4_2011 - Name Section Rec TA Side 1 of 4 Ch 1b Problem...

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