Use internal energy (U) when a process happens at constant volume, and use enthalpy (H) when it happens at constant pressure. That single distinction drives nearly every decision about which quantity to apply in a thermodynamics problem. The reason comes down to what each quantity equals under those specific conditions: at constant volume, the heat exchanged equals the change in internal energy; at constant pressure, the heat exchanged equals the change in enthalpy.
How the Two Quantities Relate
Internal energy is the total kinetic and potential energy of all the particles in a system. Enthalpy is defined as internal energy plus the product of pressure and volume:
H = U + PV
That PV term is what makes enthalpy useful. It automatically accounts for the energy a system spends (or gains) when it expands or compresses against a constant external pressure. Internal energy doesn’t include that pressure-volume work, so when volume changes matter, you’d need to track them separately. Enthalpy folds them in for you.
Constant Volume: Use Internal Energy
When the volume of a system can’t change, no expansion or compression work is done. The first law of thermodynamics says:
ΔU = q + w
With no work (w = 0), the change in internal energy equals the heat transferred: ΔU = q. This makes internal energy the natural quantity to use for rigid, sealed containers. A bomb calorimeter is the classic example. It’s a thick-walled steel vessel that holds volume fixed while a reaction takes place inside. The heat you measure from a bomb calorimeter gives you ΔU directly, not ΔH.
Any process where the container is rigid and sealed, such as a gas reacting inside a closed metal vessel, is a constant-volume scenario. Internal energy is the correct bookkeeping tool here because it captures all the energy exchange without needing to worry about pressure-volume work that isn’t happening.
Constant Pressure: Use Enthalpy
Most chemistry happens in open containers on a lab bench, meaning the system is exposed to atmospheric pressure. When pressure stays constant, the math works out so that:
ΔH = q (at constant pressure)
This is why nearly every thermochemistry table you’ll encounter lists enthalpy changes rather than internal energy changes. Reactions in beakers, test tubes, and open flasks all occur at roughly constant atmospheric pressure. A coffee cup calorimeter, which is just an insulated open container, measures enthalpy change for exactly this reason.
Phase transitions follow the same logic. Boiling water in an open pot happens at atmospheric pressure, so the energy required is reported as an enthalpy of vaporization. Melting ice on a countertop is described by an enthalpy of fusion. In both cases, the substance changes volume as it transitions between phases, and enthalpy captures that expansion work automatically.
Open Systems With Flow: Enthalpy Wins
Engineering applications add another reason to prefer enthalpy. In open flow systems like turbines, compressors, and jet engines, fluid continuously enters and exits. Pushing that fluid across the system boundary requires energy called “flow work,” equal to the pressure times the volume of the fluid moving through. Enthalpy naturally bundles internal energy and flow work into a single term, which is why the steady-flow energy equation used by engineers is written in terms of enthalpy rather than internal energy.
As MIT’s thermodynamics materials put it, enthalpy is most useful for separating flow work from external work like the shaft work a turbine produces. Without enthalpy, you’d have to track the PV contribution of every fluid packet entering and leaving the system. With enthalpy, that bookkeeping is built in.
When the Difference Is Negligible
For reactions involving only solids and liquids, the volume change during a reaction is tiny. Since ΔH = ΔU + Δ(PV), and the PV change for condensed phases is extremely small compared to the energy changes involved, ΔH and ΔU are nearly identical. In these cases it barely matters which one you use, though convention still favors enthalpy because most reactions occur in open containers.
The difference becomes significant when gases are produced or consumed. For ideal gases, the relationship simplifies to:
ΔH = ΔU + Δn(RT)
Here, Δn is the change in the number of moles of gas during the reaction, R is the gas constant, and T is temperature. If a reaction produces two moles of gas where there was one before, Δn = 1, and ΔH will be noticeably larger than ΔU. If the number of gas moles doesn’t change, ΔH and ΔU are again essentially equal even with gases present.
Quick Decision Guide
- Rigid sealed container (constant volume): Use ΔU. Heat measured equals the change in internal energy.
- Open container or atmosphere-exposed system (constant pressure): Use ΔH. Heat measured equals the change in enthalpy.
- Flow systems like turbines and compressors: Use H. It accounts for flow work automatically.
- Reactions with only solids and liquids: Either works. The numerical difference is negligible, but convention uses ΔH.
- Reactions producing or consuming gas at constant pressure: Use ΔH, and convert to ΔU with the Δn(RT) relationship if needed.
- Bomb calorimetry data: The raw measurement gives ΔU. Convert to ΔH using ΔH = ΔU + Δn(RT) if you need the constant-pressure value.
Why Enthalpy Is More Common in Practice
If you’re wondering why textbooks seem to default to enthalpy, the reason is practical. The vast majority of real-world processes, from industrial chemical reactors to biological systems to weather patterns, occur at or near constant pressure. Maintaining constant volume requires a sealed rigid container, which is a more specialized setup. Enthalpy was invented precisely because internal energy, while more fundamental, isn’t the most convenient quantity for the conditions under which most chemistry and engineering actually happen.
Internal energy remains the more fundamental thermodynamic quantity. It appears directly in the first law and doesn’t depend on any assumptions about pressure or volume constraints. Enthalpy is a derived convenience function built on top of it. Understanding both, and knowing which conditions call for which, is the key to setting up any thermodynamics problem correctly.