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17 Nov 2019
thermal!
(60 points) Even at low density, real gases don't quite obey the ideal gas law. A systematic way to account for deviations from ideal behavior is the virial expansion: B(I) C(T) V In (vin) where the functions B(m, CIT and so on are called the virial coefficients. When the density of the gas is fairly low, so that the volume per mole is large, eachterm in the series is much smaller than the one before. In many situations its sufficient to omit the third term and concentrate on the second, whose coefficient B(T is called the second virial coefficient. Below are some measured values of the second virial coefficient for nitrogen (N2): 100 -160 200 35 300 -4.2 400 9.0 I500 169 600 21.3 a) For each temperature in the table, compute the second term in the virial equation, B(T/(V/n), for nitrogen at atmospheric pressure. Discuss the validity of the ideal gas law under these conditions. b) Think about the forces between molecules, and explain why we might expect B(T) to be negative at low temperatures but positive at high temperatures. It may help to do part c first and come back tothis one. c) Any proposed relation between P, Vand Tlike the ideal gas law or the virial equation is called an equation of state. Another famous equation of state, which is qualitatively accurate even for dense fluids, isthe van der Waals equation an (V -nb) nRT P+
thermal!
(60 points) Even at low density, real gases don't quite obey the ideal gas law. A systematic way to account for deviations from ideal behavior is the virial expansion: B(I) C(T) V In (vin) where the functions B(m, CIT and so on are called the virial coefficients. When the density of the gas is fairly low, so that the volume per mole is large, eachterm in the series is much smaller than the one before. In many situations its sufficient to omit the third term and concentrate on the second, whose coefficient B(T is called the second virial coefficient. Below are some measured values of the second virial coefficient for nitrogen (N2): 100 -160 200 35 300 -4.2 400 9.0 I500 169 600 21.3 a) For each temperature in the table, compute the second term in the virial equation, B(T/(V/n), for nitrogen at atmospheric pressure. Discuss the validity of the ideal gas law under these conditions. b) Think about the forces between molecules, and explain why we might expect B(T) to be negative at low temperatures but positive at high temperatures. It may help to do part c first and come back tothis one. c) Any proposed relation between P, Vand Tlike the ideal gas law or the virial equation is called an equation of state. Another famous equation of state, which is qualitatively accurate even for dense fluids, isthe van der Waals equation an (V -nb) nRT P+
Hubert KochLv2
16 Jul 2019