Chapter2, Lesson F - Another Application of Equations of State

2F-2 :	An Application of Equations of State								6 pts

Ten kilograms of 600oC steam is contained in a 182 L tank. Find the pressure using:

a.)	The Ideal Gas EOS
b.)	The van der Waal EOS
c.)	The Soave-Redlich-Kwong EOS
d.)	The Compressibility Factor EOS
e.)	The Steam Tables

Read :	Not much to say here.

Given :	m	10	kg			V	182	L
	T	600	oC				0.182	m3

Part a.)	Ideal Gas EOS :			Eqn 1		Solve for pressure :			Eqn 2

	We must determine the molar volume before we can use Eqn 2 to answer the question.

	Use the definition of molar volume:								Eqn 3

	Where :								Eqn 4

	MW	18.016	g H2O / mol H2O				n	555.06	mol H2O
							V	3.28E-04	m3/mol

	Now, plug values back into Eqn 2.						R	8.314	J/mol-K
	Be careful with the units.						T	873.15	K
							P	2.21E+07	Pa

Answer :							P	22.1	MPa

Part b.)	van der Waal EOS :								Eqn 5

	We can determine the values of a and b, which are constants that depend only on the chemical species in the system, from the following equations.


			Eqn 6			Tc	647.4	K
						Pc	2.21E+07	Pa
						a	0.5530	Pa-mol2/m6
			Eqn 7			b	3.04E-05	m3/mol

	Now, we can plug the constants a and b into Eqn 5 to determine the pressure.

Answer :							P	19.3	MPa

Part c.)	Redlich-Kwong EOS :								Eqn 8

	We can determine the values of a, b and α, which are constants that depend only on the chemical species in the system, from the following equations.


					Eqn 9				Eqn 10

	Now, plug values into Eqns 8 -10 :

	a	14.25855	Pa-m6-K1/2/mol2				b	2.110E-05	m3/mol
Answer :	P	19.4	MPa

Part d.)	Compressibility EOS :			Given TR and the ideal reduced molar volume, use the compressibility charts to evaluate either PR or the compressibility, Z


			Eqn 11						Eqn 12

	TR	1.3487
	Defiition of the ideal reduced molar volume :								Eqn 13

						VRideal	1.3463

	Read the Generalized Compressibility Chart for PR = 0 to 1 :						PR	0.88
							Z	0.885

	We can use the definition of PR to calculate P :								Eqn 14

									Eqn 15

Answer :							P	19.4	MPa

	Or, we can use Z and its definition to determine P :								Eqn 16

Answer :							P	19.6	MPa

Part e.)	The Steam Tables provide the best available estimate of the pressure in the tank.

	Because T > Tc, the properties of the water in the tank must be obtained from the superheated vapor table, even though the water is actually a supercritical fluid in this system.


	At this point we can make use of the fact that we have a pretty good idea of what the actual pressure is in the tank (from parts a-d) or we can scan the spuerheated vapor tables to determine which two pressures bracket our known value of the specific volume.



	In either case, we begin by converting the molar volume into a specific volume :
									Eqn 17

	Using the MW of water from part a yields :						v	1.820E-05	m3/g
							v	1.820E-02	m3/kg

	The Superheated Steam Table gives us :

	At P =	15	MPa		and		At P =	20	MPa
	v =	0.02491	m3/kg				v =	0.01818	m3/kg

Answer :	We can determine the pressure in our tank by interpolation :						P	19.99	MPa

							P	20.0	MPa

Example Problem with Complete Solution