Differential expression: Does it make sense?

AI Thread Summary
The discussion centers on the mathematical validity of the expression dW=Pd2V, which is questioned for its coherence. The original poster asserts that this formulation lacks meaning, contrasting it with the established equation dW=PdV and its integral form W=∫PdV. They emphasize that since volume (V) is an independent variable and pressure (P) is a function of V, equating a first differential to a second differential is not mathematically sound. The consensus is that the expression dW=Pd2V does not hold up under scrutiny. Overall, the thread highlights the importance of proper mathematical notation in differential expressions.
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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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