Concept explainers
The ideal gas equation of state is very simple, but its range of applicability is limited. A more accurate but complicated equation is the Van der Waals equation of state given by
where a and b are constants depending on critical pressure and temperatures of the gas. Predict the coefficient of compressibility of nitrogen gas at
To compare: the coefficient of compressibility of nitrogen gas by using ideal gas equation and Van der Waals equation.
Answer to Problem 52P
The coefficient of compressibility of nitrogen gas by using ideal gas equation is calculated as
The coefficient of compressibility of nitrogen gas by using Van der Waals equation is calculated as
Error occurred by comparing is
Explanation of Solution
Given information:
The temperature of the nitrogen gas is
Write the expression for Van der Waals equation.
Here, constants depending on critical pressure and temperature are
Write the expression for coefficient of compressibility for real gas equation.
Here, rate of change of pressure with respect to specific volume at temperature
Substitute
Substitute
Write the expression ideal gas Equation.
Write the expression for coefficient of compressibility for ideal gas at constant pressure.
Substitute
Write the expression for percentage error.
Refer to Table A-1 “Molar mass, gas constant and ideal gas specific heats of some substances” to obtain the value for gas constant as
Substitute
Substitute
Substitute
Conclusion:
The coefficient of compressibility of nitrogen gas by using ideal gas equation is calculated as
The coefficient of compressibility of nitrogen gas by using Van der Waals equation is calculated as
Error occurred by comparing is
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Chapter 2 Solutions
Fluid Mechanics Fundamentals And Applications
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