Solve Van der Waals Gas Homework: a) & b)

In summary, the conversation discusses a task involving the Cpm and Cvm of gases, and how to show that Cpm - Cvm = R is valid for an ideal gas. The conversation also mentions using the triple product rule to deduce Cpm - Cvm for a Van der Waals gas. The person has solved a) but needs help with b). The conversation ends with suggestions on how to approach the problem and a thank you.
  • #1
krootox217
51
2

Homework Statement


Hi, I have the following task:
43921_adfda.JPG


Translated into English, that means:

" For Cpm and Cvm of gases the following relationship is true: (1)
a) Show with the relationship (1), that for an ideal gas Cpm - Cvm = R is valid
b) Deduce from equation (1) and the tripple product rule Cpm - Cvm for a Van der Waals gas (dependent on Vm, T and also R, a and b)"

I managed to solve a) but I don't know how to solve b)
Can someone help me?

Homework Equations


Tripple product rule: https://en.wikipedia.org/wiki/Triple_product_rule
Van der Waals equation: https://de.wikipedia.org/wiki/Van-der-Waals-Gleichung

The Attempt at a Solution


see above
 
Physics news on Phys.org
  • #2
Show us what you did so far, please. That way we can better help you.

Chet
 
  • #3
For a) I used p*Vm=RT

then I solved the equation once for p and once for Vm, and did the partial derivatives, which yielded T*(R/p)*(R/Vm) = Cpm- Cvm = (T*R2)/(p*Vm)

and then I said p*Vm=R*T and i reduced the fraction, which yielded Cpm- Cvm = R

But I don't understand how to start in the second task, could you help me?
 
  • #4
I would start out by evaluating each of the partial derivatives in Eqn. 1 and see what I get. If that doesn't give me what I'm looking for, I would start thinking about ways in which the triple product rule might get me to where I want to be. Maybe you're going to have to "play with the math" at little.

Chet
 
  • #5
Did I understand you correctly that I should do the same as in a), but this time not with the ideal gas equation, but with the van der waals equation?
 
  • #6
krootox217 said:
Did I understand you correctly that I should do the same as in a), but this time not with the ideal gas equation, but with the van der waals equation?
Sure. The problem statement indicates that the final answer should include all the parameters except for P. To me, this means that the first partial derivative in Eqn. 1 might be troublesome. See how it all plays out. Start by evaluating the two partial derivatives in equation 1 based on the van der waals equation.
 
  • Like
Likes krootox217
  • #7
Ok, thanks a lot! :)
 

1. What is Van der Waals gas?

Van der Waals gas is a type of gas that is composed of particles with non-zero volumes and that experience intermolecular attractions. Unlike an ideal gas, Van der Waals gas takes into account the volume of particles and their interaction with each other.

2. What is the Van der Waals equation?

The Van der Waals equation is a mathematical expression that describes the behavior of a Van der Waals gas. It takes into account the volume of particles and their attraction to each other, and is given by: (P + a/V^2)(V - b) = RT, where P is pressure, V is volume, a is a constant related to intermolecular forces, b is a constant related to the volume of particles, R is the gas constant, and T is temperature.

3. How is the Van der Waals equation derived?

The Van der Waals equation is derived by making corrections to the ideal gas law. The ideal gas law assumes that particles have zero volume and do not interact with each other. By incorporating corrections for particle volume and intermolecular forces, the Van der Waals equation provides a more accurate description of real gases.

4. How do you solve for the variables in the Van der Waals equation?

To solve for the variables in the Van der Waals equation, you can use algebraic manipulation to rearrange the equation and isolate the variable you are solving for. It is important to note that the constants a and b will vary for different gases, and can be found in tables or given in the problem.

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

The Van der Waals equation is commonly used in thermodynamics and chemical engineering to model the behavior of real gases. It is also used in the study of phase transitions and critical points. Additionally, the Van der Waals equation can be applied to the design of industrial processes, such as the production of liquefied gases.

Similar threads

Heat Capacity of a Van Der Waals' gas in an Open system
    • Advanced Physics Homework Help
Replies
6
Views
3K
Relation between heat capacities and van der Waals equation
    • Advanced Physics Homework Help
Replies
23
Views
9K
A I'm trying to follow the proof given in Box 5.3 of MCP (Thorne/Blandford)
    • Thermodynamics
Replies
4
Views
235
Equilibrium volume of two differential van der Waal gases
    • Advanced Physics Homework Help
Replies
7
Views
2K
Rearranging variables Van Der Waals EoS into new variables
    • Advanced Physics Homework Help
Replies
4
Views
3K
Verifying properties of Van der Waals Gas
    • Introductory Physics Homework Help
Replies
2
Views
811
Solving Maxwell Relations Homework with Van der Waals Gas
    • Advanced Physics Homework Help
Replies
2
Views
2K
What is the molecular diameter of hydrogen using Van der Waals coefficients?
    • Advanced Physics Homework Help
Replies
2
Views
3K
I Wall material effect on Van der Waals gas?
    • Classical Physics
Replies
23
Views
1K
Is the Entropy in a Free Expansion Affected by the Gas Type?
    • Advanced Physics Homework Help
Replies
8
Views
2K

Hot Threads

Recent Insights

Back
Top