Working out the cp cv difference for van der waals equation

In summary, the conversation involves brainstorming for ideas to solve a problem that involves finding the partial derivative of volume with respect to temperature. The individual has already tried one approach, but it was unsuccessful due to complications with pressure substitutions. They are seeking guidance and have shared a picture with all the relevant information.
  • #1
imagemania
27
0

Homework Statement


I've put all the information on the picture as i already created on there in an attempt to help brain storm some ideas that didn't work ...

http://dl.dropbox.com/u/48169762/Capture.PNG [Broken]

Homework Equations



All on picture :)
http://dl.dropbox.com/u/48169762/Capture.PNG [Broken]

The Attempt at a Solution



Working out [itex]\frac{\partial V}{\partial T}[/itex] via its inverse first - but it didn't work (extremly messy given pressure substitutions etc.) - as explainedd on the picture.

Any guidence is much appreciated!
 
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  • #2
Ok, I've had another look at this problem and I'm still struggling, here's my idea:

[PLAIN]http://dl.dropbox.com/u/48169762/Capture3.PNG [Broken]
 
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1. What is the difference between cp and cv in the Van der Waals equation?

The symbols cp and cv in the Van der Waals equation refer to the heat capacity at constant pressure and constant volume, respectively. These are properties of a substance that describe how much heat is needed to change its temperature at a constant pressure or volume. The main difference between the two is that cp takes into account the work done by the substance when it expands, while cv does not.

2. How do you calculate the cp and cv values for the Van der Waals equation?

The values for cp and cv in the Van der Waals equation can be calculated using the following equations:

cp = (aR^2T^2)/(V-b)^2

cv = (aR^2T)/(V-b)

Where a and b are the Van der Waals constants, R is the gas constant, T is the temperature, and V is the volume of the substance.

3. Why is it important to calculate the cp and cv values in the Van der Waals equation?

The cp and cv values are important because they help us understand the thermodynamic behavior of a substance. These values can be used to calculate other thermodynamic properties, such as enthalpy and entropy, which are important in engineering and industrial processes.

4. How does the Van der Waals equation differ from the ideal gas law?

The ideal gas law assumes that gases behave perfectly, with no interactions between molecules. The Van der Waals equation takes into account the interactions between gas molecules, which can cause deviations from ideal behavior at high pressures and low temperatures. This makes the Van der Waals equation more accurate for describing real gases.

5. What are some applications of the Van der Waals equation?

The Van der Waals equation is commonly used in chemical engineering and thermodynamics to model the behavior of real gases. It is also used in the study of phase transitions and the properties of liquids and solids. Additionally, the equation has applications in the design and optimization of industrial processes, such as in the production of liquefied gases.

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