First Law of Thermodynamics

W is energy, dW is work.

If PV=nRT, then nRT = W = energy. This part makes sense to me now. Thank you.

Since in a closed system, n, R are constant, you can replace one of the other 2 variables with this equality. (eg. P = T/V) and thus eliminate one of the 3 partial derivatives (dT, dP, dV)

In an ideal gas, PV = nRT.

Then:

-W = PV = nRT
- dW = nR(dT) = VdP + PdV.

How did you cancel only PdV or VdP, without canceling the other term, by replacement? Also, this new equation found through substitution doesn't really do anything. It basically states that total energy is the energy of all the molecules, which is really circular.

_____


And what about a real gas:





The equation doesn't cancel out to PV=nRT.