Stuck on Real Gas Problem Derivatives?

In summary, the real gas problem refers to the deviation of real gases from ideal gas behavior at high pressures and low temperatures. This can cause errors in calculations and predictions of gas behavior and is addressed by using real gas models such as the van der Waals, Redlich-Kwong, and Peng-Robinson equations. To solve real gas problems in homework, one can use the appropriate model and consider other relevant factors. Understanding the real gas problem is important in various fields, including chemical engineering, environmental science, and physics, for more accurate predictions in real-life applications.
  • #1
krootox217
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Homework Statement



The task is the following:

DqyYiM7.png


Homework Equations

The Attempt at a Solution



I calculated the derivatives for Vm (crit) and set them = 0, but somehow I can't solve the equation to obtain Vm (crit) on one side alone.

This is how far i managed to do it:

jyTvnaB.png


Can someone help me?
 
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  • #2
One approach: For each equation move the second term on the left to the right side. Then divide the two equations.
 
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  • #3
Wow, thanks!

I totally forgot that method
 

FAQ: Stuck on Real Gas Problem Derivatives?

1. What is the real gas problem?

The real gas problem is the deviation of real gases from ideal gas behavior at high pressures and low temperatures. This can be attributed to factors such as molecular size, intermolecular forces, and the volume occupied by the gas molecules.

2. How does the real gas problem affect gas behavior?

The real gas problem causes real gases to deviate from the ideal gas law, which states that at a constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of gas present. This deviation can lead to errors in calculations and predictions of gas behavior.

3. What are some common real gas models used to solve the real gas problem?

Some common real gas models include the van der Waals equation, the Redlich-Kwong equation, and the Peng-Robinson equation. These models take into account factors such as molecular size and intermolecular forces to better predict gas behavior at high pressures and low temperatures.

4. How can I solve real gas problems in my homework?

To solve real gas problems in homework, you can use the appropriate real gas model and plug in the given values for pressure, temperature, and volume. You may also need to consider any other relevant factors, such as the number of moles of gas present or the gas constant.

5. What are some real-life applications of understanding the real gas problem?

Understanding the real gas problem is important in many fields, such as chemical engineering, environmental science, and physics. It allows for more accurate predictions of gas behavior in real-world situations, such as in industrial processes or in the Earth's atmosphere.

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