Turning the ideal has equation into differential

[Guest]

Hello everyone, just having a dumb question about this, it’s from the physics course.

On the book it says that from the ideal gas equation, P.V=n.R.T and then, calculating the total differential, it ends being P.dV+V.dP=n.R.dT

Any hints on how they did it? Can’t figure it and it’s harder this way to study it because I have to memorize every equation of each step, I mean it’s simpler for me only remembering what’s the first equation and what to do in every step than remembering every full equation of each of these steps.

Huge thanks

[Guest]

Hello, please check this out. Not 100 percent sure if it’s the correct answer we’re looking for but btw

[Guest]

Hello, please check this out. Not 100 percent sure if it’s the correct answer we’re looking for but btw

Just to complete it, in the first term I took out of the differentials the constants (V, n, R) because when you do partial derivatives you do it respect to one variable and keep the others as constants. In the second term, V is the variable and therefore we can now took P out of the way as a constant and keep V as the variable for this specific term. Please check it out.

[HallsofIvy]

First, n and R are constants, not variables. P, V, and T are the variables. Second, if X= Y then dX= dY so d(PV)= d(nRT). On the left the "product rule" of differential Calculus gives d(VT)= dVT+ VdT. On the right, since n and R are constants, d(nRT)= nRdT.

Putting those together, dVT+ VdT= nRdT.