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The Enthalpy Calculator computes the enthalpy of a thermodynamic system or the enthalpy change during a process. Enthalpy, denoted $$H$$, is a state function that combines a system's internal energy with the work needed to maintain its volume against external pressure: $$H = U + PV$$
Enthalpy is arguably the most practical thermodynamic quantity in chemistry and engineering because most processes occur at constant pressure (open to the atmosphere). Under constant pressure conditions, the heat exchanged equals the enthalpy change: $$Q_p = \Delta H$$. This makes enthalpy directly measurable using calorimetry and immensely useful for energy accounting.
This calculator offers two computation modes. The first mode calculates absolute enthalpy from the internal energy, pressure, and volume using $$H = U + PV$$. The second mode computes the enthalpy change for an ideal gas or substance at constant pressure using $$\Delta H = nC_p\Delta T$$, where $$n$$ is the number of moles, $$C_p$$ is the molar heat capacity at constant pressure, and $$\Delta T$$ is the temperature change.
Enthalpy appears throughout science and engineering. In chemistry, standard enthalpies of formation and reaction (ΔH°) determine whether reactions release or absorb heat (exothermic vs. endothermic). In HVAC engineering, enthalpy of moist air determines cooling and dehumidification loads. In power engineering, steam tables provide enthalpy values at every point in a Rankine cycle. In food science, enthalpy changes govern cooking, freezing, and pasteurization processes.
A positive enthalpy change (ΔH > 0) indicates an endothermic process (heat absorbed), while a negative value (ΔH < 0) indicates an exothermic process (heat released). For example, melting ice has ΔH = +6.01 kJ/mol, and combustion of methane has ΔH = −890 kJ/mol. This calculator handles both scenarios, providing results in joules and kilojoules for convenient use across different scales.
The enthalpy calculator uses two fundamental thermodynamic relationships:
Mode 1: Definition of Enthalpy
$$H = U + PV$$
where $$U$$ is the internal energy (J), $$P$$ is the pressure (Pa), and $$V$$ is the volume (m³). The PV term represents the work required to make room for the system against external pressure.
Mode 2: Enthalpy Change at Constant Pressure
$$\Delta H = nC_p\Delta T$$
where $$n$$ is the number of moles, $$C_p$$ is the molar heat capacity at constant pressure (J/(mol·K)), and $$\Delta T = T_2 - T_1$$ is the temperature change (K).
For an ideal gas at constant pressure, $$\Delta H = Q_p$$ (the heat transferred at constant pressure equals the enthalpy change). This is why enthalpy is so useful in chemistry: most reactions occur at atmospheric pressure, so the heat of reaction equals ΔH.
In Mode 1, the result is the absolute enthalpy of the system in its current state. The PV term shows how much of the enthalpy is due to the pressure-volume work. For ideal gases at moderate pressures, PV = nRT, so the PV term is significant. In Mode 2, the result is the enthalpy change during heating or cooling. Positive ΔH means the substance absorbed heat (endothermic); negative ΔH means it released heat (exothermic). Typical values: heating 1 mol of air by 100 K gives ΔH ≈ 2910 J. For comparison, the enthalpy of vaporization of water is 40,700 J/mol.
Inputs
Results
One mole of an ideal monatomic gas at 25°C (U = 3/2 RT = 3718 J, V = 0.02445 m³ at 1 atm). The enthalpy H = U + PV = 6195 J. The PV term (2477 J = RT) accounts for about 40% of the enthalpy.
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Two moles of nitrogen gas (Cp = 29.1 J/(mol·K)) are heated by 200 K at constant pressure. The enthalpy change is 11,640 J (11.64 kJ), which equals the heat absorbed from the surroundings.
Internal energy U is the total microscopic energy of a system (kinetic + potential energy of all molecules). Enthalpy H = U + PV adds the pressure-volume work term. The difference matters at constant pressure: the heat added equals ΔH (not ΔU), because some energy goes into expanding the system against atmospheric pressure. For solids and liquids, PV is small, so H ≈ U. For gases, the PV term is significant—for an ideal gas, PV = nRT.
A negative ΔH indicates an exothermic process—the system releases heat to its surroundings. Examples include combustion reactions (ΔH_combustion of methane = −890 kJ/mol), neutralization of acids and bases, and condensation of steam to water (ΔH = −40.7 kJ/mol). Exothermic reactions feel warm and tend to be spontaneous at low temperatures.
Most chemical reactions occur at constant atmospheric pressure (in open beakers, reactors, or the human body). Under constant pressure, the heat of reaction equals ΔH, making it directly measurable with a calorimeter. Internal energy change (ΔU) equals the heat only at constant volume, which is less common experimentally. Additionally, standard enthalpy tables and Hess's Law make it easy to calculate ΔH for any reaction from tabulated formation enthalpies.
C_p is the molar heat capacity at constant pressure—the energy needed to raise one mole by one kelvin while pressure stays constant. C_v is the heat capacity at constant volume. For ideal gases, C_p = C_v + R, where R = 8.314 J/(mol·K). C_p > C_v because at constant pressure, some heat goes into expansion work. For monatomic ideal gases, C_v = 3R/2 and C_p = 5R/2. For diatomic gases (like N₂, O₂), C_p ≈ 7R/2 = 29.1 J/(mol·K).
Standard state conditions are 1 bar (100 kPa) pressure and a specified temperature, usually 25°C (298.15 K). Standard enthalpy values are denoted with a superscript degree symbol: ΔH°. The standard enthalpy of formation (ΔH°_f) is the enthalpy change when one mole of a compound is formed from its elements in their standard states. By convention, ΔH°_f = 0 for elements in their most stable form.
In power engineering, steam tables provide enthalpy values at every point in Rankine and Brayton cycles, allowing engineers to calculate work output and efficiency. In HVAC, enthalpy of moist air determines cooling loads and dehumidification requirements. In chemical engineering, enthalpy balances around reactors, heat exchangers, and distillation columns determine energy requirements and heat integration opportunities. In food processing, enthalpy calculations govern pasteurization, sterilization, and freezing processes.
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