Differential expression: Does it make sense?

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    Differential Expression
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The discussion centers on the mathematical validity of the expression dW=Pd2V, which is deemed nonsensical by participants. The correct formulation is established as dW=PdV, leading to the integral W=∫PdV. The consensus is that a first differential cannot equal a second differential, emphasizing the importance of understanding the distinction between these mathematical concepts.

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rollingstein
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I saw someone write this:

dW=Pd2V

I think this doesn't make any sense mathematically; but I wanted to check. Is this mathematically meaningful at all?

This I understand:

dW=PdV

W=∫PdV

But for dW=Pd2V I cannot see how one could proceed.

Here V is an independent variable; P=f(V).
 
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No, that doesn't make sense. You cannot have a "first differential" equal to a "second differentrial.
 
HallsofIvy said:
No, that doesn't make sense. You cannot have a "first differential" equal to a "second differentrial.

Thanks.
 

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