Q and W for Van-der-Waals Gases

In summary, The conversation involves a student asking for help with calculating Q and W for an isothermal expansion of a Van-der-Waals gas. The expert suggests using the basic formula for calculating work in thermodynamics and checking the results using the ideal gas law. The student also asks about using Wolfram Alpha for integration and the expert confirms that the small change in the calculated delta U is possible for ideal gases. The student thanks the expert for their help.
  • #1
krootox217
51
2

Homework Statement


I have the following task:

43921_1.PNG


Homework Equations

The Attempt at a Solution



I already managed to calculate Delta Um, but how do I calculate Q und W. Can I use the equations for the isothermic expansion for ideal gases, even if this are Van-der-Waals Gases?
 
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  • #2
Hello. Welcome to PF!

What is the most basic formula you know for calculating the work done by a system for any quasi-static process? Hint: This formula was probably presented when you first introduced the concept of work in thermodynamics.
 
  • #3
e701045752be3b1a02f4255078f9754e.png

This one?
 
  • #4
krootox217 said:
e701045752be3b1a02f4255078f9754e.png

This one?
Yes. They obviously want you to assume that the expansion is reversible. Your equation is correct if W represents the work done by the surroundings on the system.

Chet
 
  • #5
Ok, thanks a lot!

therefore, Q = -W?
 
  • #6
krootox217 said:
Ok, thanks a lot!

therefore, Q = -W?
No. ΔUm is not equal to zero.

Chet
 
  • #8
krootox217 said:
This means, that delta U = Q + W and I have to subtract the Work from Delta U?I have another Question, the integral is according to Wolfram alpha -7397.55 J

http://www.wolframalpha.com/input/?i=-+integral+from+0.001+to+0.020+((8.314*298.15)/(V-(3.2*10^-5))-(0.1105)/(V^2))+dV

And I calculated a Delta U of 104.98J

Therefore my Q is 7502.55J

Are these values posible?
You don't need to ask me this. Why don't you solve the same the same problem using the ideal gas law and see how the numbers compare? Incidentally, why did you need wolframalpha to do the integration for you? Why didn't you do the integration yourself?

Chet
 
  • #9
I calculated it by myself, but I often use wolfram alpha to check my results, and in this case, the result was the same, so it was easier just to paste the wolfram alpha link :)

Well, since delta U should be =0 for ideal gases, this small change seems possible?
 
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  • #10
krootox217 said:
I calculated it by myself, but I often use wolfram alpha to check my results, and in this case, the result was the same, so it was easier just to paste the wolfram alpha link :)

Well, since delta U should be =0 for ideal gases, this small change seems possible?
Sure. Wouldn't you have expected that?

Chet
 
Last edited:
  • #11
I wasn't sure,

but now it makes sense.

Thanks a lot!
 

1. What is the difference between Q and W for Van-der-Waals gases?

Q and W both refer to different forms of energy in thermodynamics. Q stands for heat, while W stands for work. In the case of Van-der-Waals gases, Q refers to the heat absorbed or released during a process, while W refers to the work done on or by the gas.

2. How are Q and W related to each other for Van-der-Waals gases?

In thermodynamics, the first law states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system. This means that for Van-der-Waals gases, Q and W are related by the equation ΔU = Q - W.

3. What is the significance of Q and W in the behavior of Van-der-Waals gases?

Q and W play important roles in understanding the behavior of Van-der-Waals gases. The heat absorbed or released by the gas can affect its temperature, while the work done on or by the gas can change its volume. This can ultimately impact the overall behavior and properties of the gas.

4. How do changes in Q and W affect the internal energy of Van-der-Waals gases?

As mentioned before, Q and W are directly related to the internal energy of a system. An increase in Q will result in an increase in internal energy, while an increase in W will lead to a decrease in internal energy. This means that changes in Q and W can directly impact the energy state of Van-der-Waals gases.

5. Can Q and W be manipulated in Van-der-Waals gases?

Q and W can be manipulated by changing the conditions of the gas, such as pressure, temperature, and volume. For example, increasing the pressure on a gas will result in more work being done by the gas, while increasing the temperature will lead to more heat being absorbed by the gas. This can ultimately affect the behavior of Van-der-Waals gases.

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