Article — Enthalpy Calculator (ΔH = q at Constant Pressure)
Enthalpy calculator (ΔH = m × c × ΔT)
Enthalpy change ΔH equals heat exchanged q when pressure is constant. The calorimetric formula is ΔH = m × c × ΔT — mass times specific heat capacity times temperature change. For water at 4.184 J/(g·K), heating 100 g from 20 °C to 80 °C absorbs 25,104 J or 25.1 kJ of heat.
Enthalpy is one of thermodynamics' most useful state functions. It tracks the heat content of open systems — beakers on a bench, atmospheric reactions, biological processes — where pressure stays roughly atmospheric. The fact that ΔH equals q at constant pressure turns abstract energy bookkeeping into something measurable with a thermometer.
What is enthalpy?
Enthalpy (symbol H) is defined as internal energy plus pressure times volume: H = U + PV. The PV term accounts for the work done by the system against atmospheric pressure when its volume changes. Internal energy alone doesn't capture that — enthalpy does.
For solids and liquids the PV term is small, so ΔH ≈ ΔU. For gases the term matters. A combustion reaction that produces gas does work pushing back the atmosphere; enthalpy bookkeeping handles that automatically while internal energy alone would not.
The word enthalpy was coined by Heike Kamerlingh Onnes around 1909 from the Greek "enthalpein" meaning "to warm in". Onnes is better known for liquefying helium and discovering superconductivity. Both achievements required precise heat measurements, which is what enthalpy was designed to track.
The enthalpy change formula
For heating or cooling without phase change or chemical reaction, the formula is q = m × c × ΔT, where m is mass, c is specific heat capacity, and ΔT = T_final − T_initial. At constant pressure, q equals ΔH directly.
H U + PVΔH (const P) q_p (heat at const pressure)ΔH (sensible) m × c × ΔTΔH (phase) m × L (latent heat)For phase changes — melting, boiling, condensing — temperature stays constant while energy is absorbed or released. Use the latent heat formula ΔH = m × L. For water: L_fusion = 334 J/g, L_vaporization = 2,260 J/g.
Enthalpy vs heat: when ΔH = q
This identity only holds at constant pressure. Most chemistry happens in open vessels under atmospheric pressure, so ΔH = q is the default working assumption. In sealed containers (bomb calorimeters, for instance), the volume is constant instead and q equals ΔU, not ΔH. You then convert: ΔH = ΔU + Δ(PV).
Calorimetry experiments designed for ΔH use coffee-cup calorimeters — open to the atmosphere. Bomb calorimeters, sealed steel vessels with fixed volume, measure ΔU and require correction to compare against published ΔH values.
Endothermic vs exothermic enthalpy
Sign convention determines everything. Positive ΔH means the system absorbed heat from its surroundings — endothermic. Negative ΔH means heat flowed out — exothermic.
- Endothermic (ΔH > 0) — ice melting, water evaporating, photosynthesis.
- Exothermic (ΔH < 0) — combustion, freezing, neutralization, condensation.
- Combustion of glucose = −2,805 kJ/mol. Major exothermic process.
- Melting of ice = +6.01 kJ/mol. Endothermic at 0 °C.
- Vaporizing water = +40.7 kJ/mol. Major energy sink in evaporative cooling.
- Neutralizing strong acid with strong base = −57 kJ/mol. Modestly exothermic.
Hand warmers and instant cold packs use enthalpy directly. Hand warmers exploit the exothermic crystallization of supersaturated sodium acetate. Cold packs use the endothermic dissolution of ammonium nitrate in water. Both rely on a specific ΔH known to within a few percent.
Specific heat capacity values
Specific heat capacity is the energy required to raise one gram by one Kelvin. Water tops the common-substance list at 4.184 J/(g·K). That number gave rise to the original calorie definition — one calorie equals the energy needed to heat 1 g of water by 1 °C.
Metals have low specific heat. Copper at 0.385 J/(g·K) needs about a tenth as much energy per gram as water. That is why a copper pot heats fast and cools fast, while a kettle of water takes minutes to boil. Most ceramics and polymers fall between metals and water, around 0.8–2.0 J/(g·K).
Enthalpy calculation example
Heating 250 g of water from 20 °C to 100 °C for tea. ΔT = 80 °C = 80 K. q = m × c × ΔT = 250 × 4.184 × 80 = 83,680 J = 83.68 kJ. That is the heat the kettle must deliver, ignoring losses.
Compare 250 g of copper through the same temperature range: q = 250 × 0.385 × 80 = 7,700 J. Eleven times less energy than water. Same volume, very different heat capacity.
Enthalpy in chemistry and engineering
Industrial reactor design lives or dies on enthalpy bookkeeping. An exothermic synthesis releases heat that must be removed to keep the reactor stable. An endothermic process needs continuous heating. Without enthalpy tables and accurate ΔH values, runaway reactions become a real safety hazard.
Doubling the mass doubles the heat needed. Doubling the temperature change doubles it too. A common mistake: students forget that 1 kg is 1,000 g. Plugging 1 instead of 1,000 gives an answer off by a factor of 1,000. Always express mass in grams when c is in J/(g·K).
Climate science also leans heavily on enthalpy. Atmospheric latent heat — the enthalpy of water vapor — drives hurricanes, monsoons, and most severe weather. A single hurricane releases roughly 6 × 10¹⁴ watts of latent heat, equivalent to about 200 times the world's electricity production at the time.
Common enthalpy mistakes
Four errors come up repeatedly. First, mixing units — mass in grams with c in J/(kg·K) gives an answer off by a factor of 1,000. Second, sign confusion — ΔH measured from the system's perspective; what feels warm to you is heat leaving the system. Third, forgetting phase change energy when crossing a melting or boiling point; the q = mcΔT formula doesn't include latent heat. Fourth, applying constant-pressure formulas in sealed containers, where ΔU is what you actually measured.
A fifth pitfall affects undergraduate labs: thermal losses to the calorimeter itself. A coffee-cup calorimeter is a decent approximation but it still absorbs some heat. Precision work requires a calibration constant — the calorimeter's heat capacity — added to the mass term. Without that correction, measured ΔH values come in systematically low.