The work a gas does just by taking up room
We said work is a force acting through a distance. In chemistry the most common work by far is sneakier than a piston in an engine — it happens in any open flask. Whenever a reaction produces gas, that gas has to *make room for itself*, and it does so by pushing the surrounding atmosphere back. Pushing back the air takes energy. This is pressure–volume work, often called *expansion work*, and it is the kind of work that dominates ordinary chemistry done on a benchtop open to the air.
When the surrounding pressure is constant — as the atmosphere essentially is — the size of this work has a clean form: w = −P ΔV. Here P is the external pressure and ΔV is the change in volume. The minus sign is the sign convention from the last guide doing its honest job: if the gas *expands* (ΔV positive), the system does work on the surroundings, so its energy goes down and w must be negative. If the gas is *compressed* (ΔV negative), the surroundings do work on the system, energy flows in, and w comes out positive. The formula and the convention agree automatically.
Why heat at constant volume isn't what we usually measure
Let us combine the First Law with this new work. Starting from ΔU = q + w and substituting w = −P ΔV, we get ΔU = q − P ΔV. Now imagine a reaction run in a *rigid sealed bomb* so the volume cannot change: ΔV = 0, the P ΔV term vanishes, and ΔU = q. In other words, the heat measured at constant volume is exactly the change in internal energy. Clean — but inconvenient, because almost no real chemistry happens in a rigid sealed bomb. Reactions happen in open beakers, living cells, and factory vats, all sitting at constant atmospheric pressure, free to change volume.
At constant pressure the volume *can* change, so some of the energy released by a reaction quietly goes into doing expansion work on the atmosphere instead of showing up as heat. That means at constant pressure, q is no longer simply ΔU — part of the energy is siphoned off into −P ΔV. Measuring ΔU directly would force us into awkward sealed bombs. Chemists wanted a quantity whose change equals the heat we *actually* measure in an ordinary open vessel. So they invented one.
Enthalpy: a quantity tailored to the open flask
The invention is enthalpy, symbol H, defined as H = U + PV. At first that combination looks arbitrary, like someone glued internal energy to a pressure-times-volume term for no reason. But watch the magic appear under constant pressure. Tracking the change, ΔH = ΔU + P ΔV. Substitute ΔU = q − P ΔV from before, and the work terms cancel exactly: ΔH = (q − P ΔV) + P ΔV = q. So at constant pressure, ΔH = q_p, the heat exchanged. Enthalpy was engineered precisely so its change equals the easy-to-measure heat of an open-flask reaction.
Because U, P, and V are each properties of the state, their combination H = U + PV is automatically a state function too. So ΔH, like ΔU, forgets the path entirely — it depends only on the start and end states. This is why a single number can be tabulated for the enthalpy change of a reaction and trusted no matter how the reaction is actually carried out. You can think of enthalpy loosely as "the heat content available at constant pressure": not perfectly literal, but a serviceable mental picture for a beginner. The honest, precise statement is simply ΔH = q at constant pressure.
When does ΔH differ from ΔU?
A fair question: are ΔH and ΔU really different in practice, or is this just bookkeeping? The gap between them is exactly the P ΔV work. For reactions among only solids and liquids, volumes barely change, so P ΔV is tiny and ΔH ≈ ΔU to good accuracy. The two part company only when *gases are made or consumed*, because gases swallow or release a lot of volume. Burning fuel that turns liquid into a flood of hot gas, or a reaction that soaks gas up into a solid, is where the distinction earns its keep.
This is why enthalpy, not internal energy, is the everyday hero of chemistry. The next guide builds an entire toolkit — thermochemistry — on ΔH, precisely because it is the heat we read straight off a thermometer in the normal, open, constant-pressure world we actually live and work in. Internal energy is the deeper, more fundamental quantity; enthalpy is the practical one we reach for first.