# Solving for volume in Van der Waals Equation?

• NeedPhysHelp8
In summary, the conversation discusses solving for the specific volume of water steam at a given pressure and temperature using both the ideal gas equation and the van der Waals equation. The specific volume is successfully calculated using the ideal gas equation, but the individual is struggling to solve for the specific volume using the van der Waals equation. They have managed to rearrange the equation in terms of specific volume but are still unsure how to solve for it.
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?

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?

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.

## 1. What is the Van der Waals equation and why is it important in science?

The Van der Waals equation is a mathematical equation that describes the behavior of real gases, taking into account the volume of the gas particles and the intermolecular forces between them. It is important in science because it allows for a more accurate prediction of gas behavior, especially at high pressures and low temperatures, where the ideal gas law fails to accurately describe real gas behavior.

## 2. How is the Van der Waals equation different from the ideal gas law?

The ideal gas law assumes that gas particles have no volume and do not interact with each other, while the Van der Waals equation takes into account the volume of the particles and the attractive forces between them. It also includes two additional parameters, a and b, which account for the intermolecular forces and the volume of the particles, respectively.

## 3. What is the process for solving for volume in Van der Waals equation?

To solve for volume in the Van der Waals equation, you will need to know the values of pressure (P), temperature (T), and the two parameters a and b. You can rearrange the equation to solve for V, the volume, by dividing both sides by P and then using algebra to isolate V. You may also need to use the quadratic formula to solve for V if the equation has a squared term.

## 4. How do you determine the values of a and b in Van der Waals equation?

The values of a and b can be determined experimentally by measuring the critical temperature and pressure of a gas. The critical temperature (Tc) is the temperature at which a gas can no longer be liquified, and the critical pressure (Pc) is the pressure required to liquify the gas at its critical temperature. These values can then be used to calculate a and b using the following equations: a = 27/64 x (R^2 x Tc^2 / Pc) and b = R x Tc / 8 x Pc, where R is the gas constant.

## 5. Can the Van der Waals equation be used for all gases?

No, the Van der Waals equation is only applicable to real gases and is not accurate for all gases. It is most accurate for gases that have large molecular sizes and strong intermolecular forces, such as gases with polar molecules. For gases with small molecular sizes and weak intermolecular forces, the ideal gas law may be a more accurate representation of their behavior.

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