Solving for volume in Van der Waals Equation?

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SUMMARY

The discussion focuses on calculating the specific volume of water steam at 100 kPa and 500 degrees Celsius using both the ideal gas law and the Van der Waals equation. The ideal gas calculation yielded a specific volume of 3.57 m3/kg. The user successfully reformulated the Van der Waals equation to isolate specific volume but struggled with solving for v. The relevant equations discussed include the ideal gas law (pv = nRT) and the Van der Waals equation, which is expressed as (p + n2a/V2)(V - nb) = nRT.

PREREQUISITES
  • Understanding of the ideal gas law (pv = nRT)
  • Familiarity with the Van der Waals equation for real gases
  • Basic knowledge of thermodynamics and specific volume concepts
  • Ability to manipulate algebraic equations for solving variables
NEXT STEPS
  • Study the derivation and application of the Van der Waals equation in thermodynamics
  • Learn how to solve for specific volume using the Van der Waals equation
  • Explore the differences between ideal gas behavior and real gas behavior
  • Investigate the implications of using different equations of state for various gases
USEFUL FOR

Students and professionals in thermodynamics, chemical engineering, and physical chemistry who are working with gas laws and real gas behavior will benefit from this discussion.

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Solving for volume in Van der Waals Equation??

Homework Statement


Determine the specific volume, v (volume per mass[m^3/kg]) of a water steam at a pressure of 100kPa and a temperature of 500 degrees Celsius by assuming an ideal gas (pV = nRT) and by using the van der Waals equation for n moles


Homework Equations


pv = nRT
van der waals equation (p + n^2a/V^2)(V-nb) = nRT


The Attempt at a Solution


alright I got the first part no problem as i used the molar mass of air to be 18.0g/mol and I got the specific volume to be 3.57 m^3/kg. The second part of the question is confusing me because I have no clue how to solve for the volume for Van der Waals! any help please?
 
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well I was able to get Van Der Walls Equation in terms of specific volume:

(p + a/(v^2M^2)) (v- b/M) = RT/M

still can't figure out how to solve for v, specific volume?
 

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