I've been trying to understand the conceptual idea and purpose of enthalpy for the past two days.
From what I've learned, enthalpy is defined as:
$$E = U + PV$$
This leads me to my first question. Was this formula created or was it derived?
For example, the formula for kinetic energy can be derived from the equation for work (F*dx). So for enthalpy, is this formula derived from something else, or is it just a brand new idea that was simply created by someone as U + PV, because it's easier to solve this than find the internal energy for some processes (like in an open lab, where PV work is hard to measure)?
Next, the change in enthalpy is expanded as:
$$ΔE = ΔU + Δ(PV)$$ $$ΔE = Q + W + Δ(PV)$$ $$ΔE = Q - PΔV + Δ(PV)$$
From what I read, unlike internal energy, enthalpy becomes very useful when the pressure is constant. The explanations all say that this is because when pressure is constant, the -PΔV and Δ(PV) terms become equal to each other and cancel out, leaving only Q (heat).
This makes me ask: why does pressure need to be constant? If pressure is non-constant, couldn't they still cancel out? Just as a random example, if P = 2x, then wouldn't it be
$$ ΔE = Q -2xΔV + 2xΔV$$ thus cancelling out?
Secondly, why do we even need to measure enthalpy? If enthalpy is simply the heat transferred (Q) when pressure is constant, we're obviously simply ignoring the PV work done. So why introduce a new idea at all, instead of just continuing to use internal energy and heat (Q)? Many websites say things along the lines of:
"Sometimes it's hard to measure changes in internal energy because it's hard to measure the PV work done in a lab setting, since beakers and test tubes are open. So, we introduce enthalpy, which accounts for the work, and is simply heat transfer (when pressure is constant)"
Isn't the above statement just the same as saying:
"It's hard to measure work, so let's ignore work and measure heat instead"?
If so, then what benefit does measuring enthalpy give us, when we could just always measure heat transfer regardless of whether pressure is constant or not?
Please let me know if I should elaborate on my question if something is unclear. At this point, I'm so confused that I'm not even sure how to word my questions well. I spent the past 2 days trying to figure it out, but ended up getting even more confused and frustrated!