[kelvinLTR]

if X is a thermodynamic property, dX is an exact differential we were taught. I am quite new for partial derivatives as well as thermodynamics (I am a first year BSc student who've taken Math for advanced level). Can someone please explain why is dX an exact differential?

[Corribus]

Forgive the seemingly flippant reply, but I don't really understand the question.

[kelvinLTR]

does X being a thermodynamic property imply dX is an exact differential and vice versa. If so, why?

[curiouscat]

does X being a thermodynamic property imply dX is an exact differential and vice versa. If so, why?

My guess is thermo properties being state functions always define a conservative field.

Differential forms corresponding to conservative fields are exact.

[Arkcon]

I'm curious, coming from a math scholar, what would be an inexact differential?  I am not nearly good at math, but a mathematical function, applied to another function, how can that be inexact?  For example 4+5, or 9x3, their results are exact, right?  I suppose, 9 divided by 5, yeah that's not exact.  But the differentials,  I may be missing what would be inexact, so I'd like to see a theoretical inexact differential of a function.

I suppose, given that calculus was invented/discovered to describe real physical phenomena, that the derivatives have to likes "make sense."  But I can't say for sure that requires the differential to be exact.

[curiouscat]

I'm curious, coming from a math scholar, what would be an inexact differential?  I am not nearly good at math, but a mathematical function, applied to another function, how can that be inexact?  For example 4+5, or 9x3, their results are exact, right?  I suppose, 9 divided by 5, yeah that's not exact.  But the differentials,  I may be missing what would be inexact, so I'd like to see a theoretical inexact differential of a function.

I suppose, given that calculus was invented/discovered to describe real physical phenomena, that the derivatives have to likes "make sense."  But I can't say for sure that requires the differential to be exact.

I don't think exact and inexact refer to conventional accuracies but more to the mathemetical properties of these abstractions.

e.g. an integral from a to a of any differential is normally zero. But not when applied to inexact forms. e.g. differential work

Most math theorems etc. apply strictly only to exact differentials. Inexact ones are convinently treated under the same formalism so long as we are careful not to do certain things with them.