The van der Waals (vdW) equation is a cubic equation of state (CEOS) which may be used to calculate the volume or pressure conditions for a real gas: P= a = RT a v-b v² Here, v represents the molar volume of the gas, and P, R, and T' are the absolute pressure, ideal gas constant, and absolute temperature of the gas, respectively. The values a and b are component dependent an may be calculated using: 27 R²T² 64 P C and b= 1 RT 8 Pc So, when both the critical pressure (Pc) and critical temperature (Tc) are known, one can apply the vdW CEOS to give a more accurate calculate more accurate properties than the ideal gas law. One must be careful to use absolute values for the pressure & temperature (e.g., unit of K not °C) and a value for the gas constant that is consistent with the unit desired (such as R = 0.0083144598 L·bar/K·mol) Do the following: a) Calculate the molar volume (L/mol) of nitrogen gas (Pc = 33.96 bar, Tc = 126.19 K) at 5 bar and 30°C using both the ideal gas law & using the vdW CEOS. b) Calculate the molar volume (L/mol) of ammonia gas (Pc = 113.33 bar, Tc = 405.40 K) at 15 bar and 110°C using both the ideal gas law & using the vdW CEOS.

The van der Waals (vdW) equation is a cubic equation of state (CEOS) which may be used to calculate the volume or pressure conditions for a real gas: P= a = RT a v-b v² Here, v represents the molar volume of the gas, and P, R, and T' are the absolute pressure, ideal gas constant, and absolute temperature of the gas, respectively. The values a and b are component dependent an may be calculated using: 27 R²T² 64 P C and b= 1 RT 8 Pc So, when both the critical pressure (Pc) and critical temperature (Tc) are known, one can apply the vdW CEOS to give a more accurate calculate more accurate properties than the ideal gas law. One must be careful to use absolute values for the pressure & temperature (e.g., unit of K not °C) and a value for the gas constant that is consistent with the unit desired (such as R = 0.0083144598 L·bar/K·mol) Do the following: a) Calculate the molar volume (L/mol) of nitrogen gas (Pc = 33.96 bar, Tc = 126.19 K) at 5 bar and 30°C using both the ideal gas law & using the vdW CEOS. b) Calculate the molar volume (L/mol) of ammonia gas (Pc = 113.33 bar, Tc = 405.40 K) at 15 bar and 110°C using both the ideal gas law & using the vdW CEOS.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

The van der Waals (vdW) equation is a cubic equation of state (CEOS) which may be used
to calculate the volume or pressure conditions for a real gas:
P=
a =
RT a
v-b v²
Here, v represents the molar volume of the gas, and P, R, and T' are the absolute pressure,
ideal gas constant, and absolute temperature of the gas, respectively. The values a and b
are component dependent an may be calculated using:
27 R²T²
64 P
C
and b=
1 RT
8 Pc
So, when both the critical pressure (Pc) and critical temperature (Tc) are known, one can
apply the vdW CEOS to give a more accurate calculate more accurate properties than the
ideal gas law. One must be careful to use absolute values for the pressure & temperature
(e.g., unit of K not °C) and a value for the gas constant that is consistent with the unit
desired (such as R = 0.0083144598 L·bar/K·mol)
Do the following:
a) Calculate the molar volume (L/mol) of nitrogen gas (Pc = 33.96 bar, Tc = 126.19 K) at
5 bar and 30°C using both the ideal gas law & using the vdW CEOS.
b)
Calculate the molar volume (L/mol) of ammonia gas (Pc = 113.33 bar, Tc = 405.40 K)
at 15 bar and 110°C using both the ideal gas law & using the vdW CEOS.

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