Van Der Waals equation solving for V

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SUMMARY

The discussion centers on solving the Van Der Waals equation for volume (V) given by the formula P = RT/(V-b) - a/V^2. A participant has derived an intermediate equation: RTV^2 - aV + ab = P(V^3 - V^2b) but is struggling to isolate V. Suggestions include using parentheses for clarity and collecting terms to form a cubic equation in V, which can then be solved using factoring techniques.

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  • Understanding of the Van Der Waals equation
  • Familiarity with algebraic manipulation and factoring
  • Knowledge of cubic equations and their solutions
  • Basic thermodynamics concepts related to pressure, volume, and temperature
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  • Study methods for solving cubic equations, including Cardano's method
  • Review algebraic techniques for factoring polynomials
  • Explore the implications of the Van Der Waals equation in real gas behavior
  • Learn about numerical methods for approximating solutions to complex equations
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Students in chemistry or physics, particularly those studying thermodynamics and gas laws, as well as educators looking for problem-solving strategies related to the Van Der Waals equation.

George3
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Homework Statement



P = RT/(V-b) - a/V^2

Ive been trying to solve this for V and just can't get it.

Homework Equations




The Attempt at a Solution


IVe gotten to:
RTV^2 -aV+ab = P(V^3-V^2b)
Any Ideas?
 
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George3 said:

Homework Statement



P = RT/(V-b) - a/V^2

Ive been trying to solve this for V and just can't get it.

Homework Equations




The Attempt at a Solution


IVe gotten to:
RTV^2 -aV+ab = P(V^3-V^2b)
Any Ideas?

Could you use more parenthesis to make the equation clearer? Or is its form just as written:

P = \frac{RT}{V-b} - \frac{a}{V^2}
 
From your partial solution, it does look like that was the original form. Collect terms and factor for V would be the next steps...

()V^3 + ()V^2 + ()V + () = 0
 

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