QUESTION 3 (20 MARKS) Thermodynamic properties of water are readily available in the property tables. However,...
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QUESTION 3 (20 MARKS) Thermodynamic properties of water are readily available in the property tables. However, you are interested to know the adequacy of generic cubic equation of state, particularly the van der Waals equation of state in the prediction of specific volume of water. Given critical temperature, critical pressure, acentric factor, and molecular weight of water are 374.1 K, 220.55 bar, 0.345, and 18.015 g/mol. [Hint: R₂ = 83.14 cm³. bar/(mol. K)] (a) Given that the vapor pressure of water at 100°C is 1.0142 bar (101.42 kPa). Calculate the numerical value of all required parameters (a(T,; w), o, , , , ß, q) in the van der Waals equation of state. (5 Marks) (b) Estimate the molar and specific volumes of saturated liquid of water at 100°C and 1.0142 bar (101.42 kPa) by using the van der Waals equation of state. Solve the equation via numerical method (simple fixed-point method) until the answer converges. (5 Marks) (c) Estimate the molar and specific volumes of saturated vapor of water at 100°C and 1.0142 bar (101.42 kPa) by using the van der Waals equation of state. Solve the equation via numerical method (simple fixed-point method) until the answer converges. (5 Marks) (d) Estimate the change of specific volume during vaporization of water at 100°C and 1.0142 bar (101.42 kPa). Compare your estimated value with the property table value. (5 Marks) QUESTION 3 (20 MARKS) Thermodynamic properties of water are readily available in the property tables. However, you are interested to know the adequacy of generic cubic equation of state, particularly the van der Waals equation of state in the prediction of specific volume of water. Given critical temperature, critical pressure, acentric factor, and molecular weight of water are 374.1 K, 220.55 bar, 0.345, and 18.015 g/mol. [Hint: R₂ = 83.14 cm³. bar/(mol. K)] (a) Given that the vapor pressure of water at 100°C is 1.0142 bar (101.42 kPa). Calculate the numerical value of all required parameters (a(T,; w), o, , , , ß, q) in the van der Waals equation of state. (5 Marks) (b) Estimate the molar and specific volumes of saturated liquid of water at 100°C and 1.0142 bar (101.42 kPa) by using the van der Waals equation of state. Solve the equation via numerical method (simple fixed-point method) until the answer converges. (5 Marks) (c) Estimate the molar and specific volumes of saturated vapor of water at 100°C and 1.0142 bar (101.42 kPa) by using the van der Waals equation of state. Solve the equation via numerical method (simple fixed-point method) until the answer converges. (5 Marks) (d) Estimate the change of specific volume during vaporization of water at 100°C and 1.0142 bar (101.42 kPa). Compare your estimated value with the property table value. (5 Marks)
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