Solving for volume in Van der Waals Equation?

[NeedPhysHelp8]

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?

 

[NeedPhysHelp8]

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?

 

[kerimek]

I would suggest approaching this problem by first understanding the van der Waals equation and how it differs from the ideal gas equation. The van der Waals equation takes into account the intermolecular forces and the finite size of gas particles, which are not considered in the ideal gas equation. This means that the van der Waals equation can provide more accurate results, especially at high pressures and low temperatures.

To solve for volume in the van der Waals equation, we need to rearrange the equation to isolate V. This can be done by first expanding the equation and then grouping terms with V on one side of the equation. This will result in a polynomial equation that can be solved using mathematical techniques such as factoring or the quadratic formula.

Alternatively, you can use a numerical method such as Newton's method to solve for the volume. This involves making an initial guess for the volume and then using iterative calculations to get closer and closer to the actual solution. This method may be more time-consuming, but it can provide a more accurate solution.

Overall, solving for volume in the van der Waals equation can be more complex compared to the ideal gas equation, but it can provide more accurate results in certain conditions. It is important to understand the differences between the two equations and how to apply them in different scenarios.