Enthalpy H = U + PV Is Natural at Constant Pressure
Heat a gas at constant pressure and part of the heat raises the internal energy while part escapes as expansion work. Enthalpy, H = U + PV, bundles those two together.
Add heat. At constant pressure the gas expands, so the heat splits between a rise in internal energy and expansion work. Not all of it goes into temperature. So to raise the temperature by the same amount, more heat is needed at constant pressure, where the piston is pushed out and part of the heat leaks away as expansion work, than in a rigid fixed-volume vessel.
Enthalpy is internal energy plus PV. Change the volume and watch the PV bar grow. H = U + PV stacks up as one state property, and for an ideal gas H too is a function of temperature alone. Unlike work or heat, H is a state property fixed by the current state alone, so the enthalpy difference between two states is always the same no matter the path taken.
Switch the two cases. At constant volume no work is done, so the heat is just ΔU. At constant pressure the heat becomes ΔH outright. Heat at constant pressure is an enthalpy change. The reaction heats listed in a chemistry book are mostly given as enthalpies for the same reason: the experiments happen at constant pressure open to the atmosphere, so the heat exchanged is exactly the enthalpy change.
Now an open system. To push fluid across the boundary you must do work against the pressure, equal to PV. Slide to push it in: this flow work is exactly PV. When water is pushed through a pipe or a pump draws fluid in, every parcel of fluid entering always carries along its share of PV, the work of shoving aside the pressure ahead.
Why bother with H? Compare with the buttons. A closed system gets by with U, but any flow in or out always drags PV flow work along. Folding that PV into U ahead of time gives H, the natural language of flow devices like pumps, turbines, and boilers. Next we move to the ideal gas. Sizing up a refrigerator or a jet engine also comes down to reading the enthalpy difference of the fluid flowing in and out, and the simplest starting point for handling that fluid is exactly the ideal gas of the next lesson.