Enthalpy Calculator

Background.

Internal energy is the energy stored inside a system — the motion of its molecules and the bonds between them. But a system sitting in the open air also occupies space, and making that space meant pushing the surroundings out of the way. Enthalpy adds that cost to the stored energy: H = U + pV, where p is the pressure the system sits at and V the volume it takes up.

The pV term is not small for gases. Twenty litres of gas at one standard atmosphere, 101,325 pascals, has pushed back the atmosphere with 2,026.5 joules of work. For a solid or liquid the term is tiny: a mole of liquid water, about 18 millilitres, carries less than 2 joules of pV at the same pressure, so its enthalpy and internal energy are almost the same number.

Chemists and engineers prefer enthalpy because of what happens when a process runs at constant pressure, as most bench reactions and many flow processes do. The heat taken in or given out then equals the change in enthalpy, not the change in internal energy, because part of any heat supplied goes into expansion work against the surroundings. That is why tables list heats of reaction, combustion and vaporisation as ΔH values, and why steam tables list specific enthalpy for every state. Air-conditioning engineers lean on it too: the cooling a coil must deliver is the drop in enthalpy of the air passing over it, read off a psychrometric chart in kilojoules per kilogram of dry air, and a large share of that drop on a humid day is water vapour condensing rather than air getting colder.

Signs follow the system. A negative ΔH means the system handed heat to its surroundings, as every combustion does; a positive one means it absorbed heat, as melting ice or the ammonium nitrate dissolving in an instant cold pack does. Tables of standard enthalpies of formation rest on one more choice: each element in its most stable form at 1 bar is assigned zero, so a compound's value is the enthalpy change of making it from its elements, and a reaction's ΔH is the products' total minus the reactants'.

The arithmetic here is just that one identity, applied to a single state. Absolute internal energy cannot be measured, only changes in it, so U is whatever value you have relative to your chosen reference, and H inherits the same reference. To find an enthalpy change, work out H for the start and end states and subtract.

What is enthalpy calculator?

Enthalpy is a thermodynamic state function defined as internal energy plus the product of pressure and volume, H = U + pV. Like internal energy it is measured in joules and depends only on the current state of the system, not on how it got there. Its practical meaning comes from its change: for a process at constant pressure with only expansion work, ΔH equals the heat exchanged with the surroundings. Enthalpy is extensive: twice the material in the same state has twice the H. Tables therefore quote it per unit amount — kilojoules per mole in chemistry, kilojoules per kilogram in steam tables and engineering, and in older American references Btu per pound, where 1 Btu/lb is exactly 2.326 kJ/kg. For an ideal gas pV equals nRT, so H = U + nRT and both depend on temperature alone; for real gases, liquids and solids, pressure enters as well. Reaction enthalpies also shift with temperature, at a rate set by the difference in heat capacity between products and reactants, which is why tables state the temperature they apply to, usually 298.15 K.

How to use this calculator.

1. 01Enter the internal energy U of the system in joules, measured from the same reference state as any table you are using. Steam tables, for instance, set the internal energy of liquid water at its triple point, 0.01 °C, to zero, so their values only mean something against each other. The page accepts only positive values, so a state below its reference — ice, on the steam-table scale — has to be added up by hand.
2. 02Enter the absolute pressure in pascals. Multiply kilopascals by 1,000 and bar by 100,000; one standard atmosphere is 101,325 Pa. Gauge pressure readings need atmospheric pressure added first.
3. 03Enter the volume the system occupies in cubic metres. Divide litres by 1,000, so 20 L is 0.02 m³.
4. 04Read the enthalpy in joules. Because U and V here are totals for the whole system, so is H; for a per-kilogram or per-mole value, enter specific or molar U and V instead.

The formula.

H = U + p × V. U is the internal energy in joules, p the absolute pressure in pascals and V the volume in cubic metres. The units fit without any conversion factor because one pascal is one newton per square metre, so pascals times cubic metres gives newton-metres, which are joules. The pV product is the work needed to create room for the system at pressure p against its surroundings. For gases at everyday pressures it can be a sizeable share of H; for liquids and solids it is usually negligible, and H is close to U. Doubling either the pressure or the volume doubles the pV contribution while leaving U unchanged. The page combines U, p and V for one state; it does not look up property data or compute a change between states.

Why the heat at constant pressure equals ΔH follows in two lines from the first law. With only expansion work, heat q added to a system raises its internal energy and pays for the expansion: q = ΔU + pΔV when p is constant. Because p does not change, pΔV is the same as Δ(pV), so q = Δ(U + pV) = ΔH. The definition holds for any substance; it is the shortcut that needs those conditions. If the pressure changes during the process, or the system does other work, such as a battery driving a current, the heat no longer equals ΔH. The same bookkeeping explains the gap between an ideal gas's two molar heat capacities: since H = U + nRT, warming a mole by one kelvin at constant pressure costs R, about 8.314 J, more than at constant volume.

A worked example.

Frequently asked questions.

References& sources.

1. [1]IUPAC Gold Book, enthalpy.
2. [2]OpenStax, Chemistry 2e, section 5.3, Enthalpy.
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.
4. [4]NIST Special Publication 811, Guide for the Use of the International System of Units, 2008 edition.
5. [5]NIST Chemistry WebBook, thermochemistry data conventions.