Concept explainers
A 3.27-m3 tank contains 100 kg of nitrogen at 175 K. Determine the pressure in the tank using (a) the idealgas equation, (b) the van der Waals equation, and (c) the Beattie-Bridgeman equation. Compare your results with the actual value of 1505 kPa.
(a)
The pressure in the tank using the ideal gas equation.
Answer to Problem 96P
The pressure in the tank using the ideal gas equation is
Explanation of Solution
Determine the specific volume in the tank.
Here, the volume of the tank is
Determine the pressure of the tank using the ideal gas equation.
Here, the universal gas constant is
Conclusion:
Refer to Table A-1 to find the gas constant, molar mass, the critical pressure, and the critical temperature of nitrogen as
Substitute
Substitue
Therefore, the error compression with the actual value is 5.5%.
Thus, the pressure in the tank using the ideal gas equation is
(b)
The pressure in the tank using the van der Waals.
Answer to Problem 96P
The pressure in the tank using the van der Waals is
Explanation of Solution
Determine the pressure in the tank using the van der Waals.
Here, the critical temperature is
Conclusion:
Substitute
Therefore, the error compression with the actual value is 0.7%.
Thus, the pressure in the tank using the van der Waals is
(c)
The pressure in the tank using the Beattie-Bridgeman equation.
Answer to Problem 96P
The pressure in the tank using the Beattie-Bridgeman equation is
Explanation of Solution
Determine the pressure in the tank using the Beattie-Bridgeman equation.
Here, the five constant are
Conclusion:
From the Table 3-4, “Constant that appear in the Beattie-Bridgeman and the Benedict-Webb-Rubin equation of state” to obtain of value of the five constant are
Substitute 136.2315 for
Therefore, the error compression with the actual value is 0.07%.
Thus, the pressure in the tank using the Beattie-Bridgeman equation is
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