Arguing work is an inexact differential

In summary, the conversation discusses the fundamental thermodynamic relation and the concept of exact and inexact differentials. The question is how to make pdV, which is inexact, into an exact differential. The suggested term to add is Vdp, but this implies that pdV is inexact unless Vdp is equal to 0. The conversation concludes with the understanding that pdV is indeed inexact.
  • #1
Sekonda
207
0
Hey,

Given the fundamental thermodynamic relation (dN=0) ; TdS=pdV+dU, I have to argue that pdV is inexact. I know that dS and dU are exact differentials and that the integral of an exact differential around a closed loop will give a zero result, not too sure where to start, the question is only a couple of marks so the answer need only be brief but my understanding is limited as to why pdV, the work, has to be an inexact differential.

Any help appreciated!

Thanks.
 
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  • #2
Hey Sekonda! :smile:

What would you add to pdV to make it an exact differential? :wink:
 
  • #3
Vdp?

I'm still not sure I'm going to have to think about this a bit more!
 
  • #4
Is this the correct term to add to pdV to make it an exact differential; if so, how does this imply that pdV is inexact?
 
  • #5
Sekonda said:
Is this the correct term to add to pdV to make it an exact differential

Yes, pdV + Vdp is an exact differential … it's exactly d(pV).

So that means that (unless Vdp = 0, ie p is constant) pdV is not exact. :smile:
 
  • #6
Ahh yes that does make sense! I'm always bad at 'arguing', 'showing' or 'proofing' questions; thanks man.

Cheers!
 

What is an inexact differential in the context of arguing work?

An inexact differential is a concept in thermodynamics that refers to a change in a system that is dependent on the path taken, rather than just the initial and final states. In the context of arguing work, it means that the amount of work done on a system may vary depending on the method used to achieve that work.

Why is it important to consider the inexactness of work when making an argument?

When arguing about work, it is crucial to consider the inexactness of work because it can affect the validity of your argument. If you fail to acknowledge the potential variations in the amount of work done, your argument may be flawed or incomplete.

How does the concept of inexact differentials apply to real-world scenarios?

In real-world scenarios, inexact differentials can be seen in various processes such as friction, heat transfer, and chemical reactions. These processes involve changes that are dependent on the path taken, making it important to consider the inexactness of work when analyzing and making arguments about them.

What are some common misconceptions about arguing work as an inexact differential?

One common misconception is that inexact differentials make work impossible to calculate or measure accurately. While the inexactness of work can make it more challenging to determine an exact value, there are methods and calculations that can be used to estimate the amount of work done on a system.

How can understanding the concept of inexact differentials improve scientific arguments about work?

Understanding the concept of inexact differentials can improve scientific arguments about work by allowing researchers to acknowledge and account for the potential variations in work. This can lead to more accurate and comprehensive arguments that consider the complexities of real-world processes.

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