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Sources & Methodology
⏱ Last reviewed: April 2026 — Specific heat values cross-verified against NIST and CRC Handbook
How to Calculate Enthalpy Change (q = mcΔT)
Enthalpy (H) is a thermodynamic property representing the total heat content of a system at constant pressure. The enthalpy change (ΔH) tells us how much heat flows into or out of a system during a physical or chemical process. Understanding enthalpy is fundamental to chemistry, chemical engineering, HVAC system design, metallurgy, and any field where heat transfer matters.
Sign convention (IUPAC):
• q > 0 (positive): Endothermic — system absorbs heat from surroundings
• q < 0 (negative): Exothermic — system releases heat to surroundings
At constant pressure: ΔH = q_p (enthalpy change equals heat at constant pressure)
What Is Specific Heat Capacity?
Specific heat capacity (c) is the amount of heat energy required to raise the temperature of 1 gram of a substance by 1 degree Celsius (or 1 Kelvin, which is the same temperature difference). It is a material property that reflects how much thermal energy a substance can store per unit mass.
Water has an exceptionally high specific heat capacity: c = 4.186 J/g·°C. This means it takes 4.186 joules to heat 1 gram of water by 1°C. By comparison, copper requires only 0.385 J/g·°C. This is why water is such an excellent coolant — it can absorb large amounts of heat with only a small temperature rise. It is also why coastal climates are milder than inland areas: the ocean can absorb and release enormous amounts of heat with minimal temperature change.
Exothermic vs Endothermic Processes
Exothermic processes (negative ΔH) release heat to the surroundings. The temperature of the surroundings increases. Common examples include:
- Combustion of fuels: methane + oxygen → CO&sub2; + H&sub2;O, ΔH = −890 kJ/mol
- Condensation of steam: water vapor → liquid water, ΔH = −40.7 kJ/mol at 100°C
- Freezing of water: liquid → ice, ΔH = −6.01 kJ/mol at 0°C
- Neutralization: HCl + NaOH → NaCl + H&sub2;O, ΔH = −57.1 kJ/mol
- Hand warmers: iron oxidation, rusting reactions
Endothermic processes (positive ΔH) absorb heat from the surroundings. The temperature of the surroundings decreases. Common examples include:
- Melting of ice: ice → liquid water, ΔH = +6.01 kJ/mol at 0°C
- Evaporation of water: liquid → vapor, ΔH = +40.7 kJ/mol at 100°C
- Photosynthesis: CO&sub2; + H&sub2;O → glucose + O&sub2; (solar energy input)
- Dissolving ammonium nitrate in water (cold packs work this way)
- Cooking an egg: denaturation of proteins requires heat input
Phase Changes and Latent Heat
The q = mcΔT formula applies only when the substance changes temperature without changing phase. When a phase change occurs (melting, boiling, condensing, freezing), the temperature remains constant even as heat flows. This heat is called latent heat, and it is calculated separately:
- Heat of fusion (melting/freezing): q = m × L_f (Water: L_f = 334 J/g)
- Heat of vaporization (boiling/condensing): q = m × L_v (Water: L_v = 2,260 J/g)
To heat 1 kg of ice at −10°C to steam at 110°C involves five stages: (1) heat ice from −10°C to 0°C, (2) melt ice at 0°C, (3) heat water from 0°C to 100°C, (4) boil water at 100°C, (5) heat steam from 100°C to 110°C. Each stage uses q = mcΔT except steps 2 and 4 which use q = mL.
Hess's Law and Enthalpy of Reaction
For chemical reactions, enthalpy change is calculated using Hess's Law: the total ΔH for a reaction is independent of the pathway taken. This allows calculation of ΔH_rxn from standard enthalpies of formation:
ΔH°_rxn = ∑ΔH°_f(products) − ∑ΔH°_f(reactants)
Standard enthalpies of formation (ΔH°_f) are tabulated for thousands of compounds. For elements in their standard states, ΔH°_f = 0 by definition. For water vapor: ΔH°_f = −241.8 kJ/mol. For liquid water: −285.8 kJ/mol. The difference (44 kJ/mol) is the enthalpy of vaporization at standard conditions.
Specific Heat Capacity Reference Table
| Substance | Specific Heat (J/g·°C) | Phase | Relative to Water |
|---|---|---|---|
| Water (liquid) | 4.186 | Liquid | Reference (1.00×) |
| Ice | 2.090 | Solid | 0.50× water |
| Steam (water vapor) | 2.010 | Gas | 0.48× water |
| Ethanol (alcohol) | 1.670 | Liquid | 0.40× water |
| Aluminum (Al) | 0.900 | Solid metal | 0.21× water |
| Glass (borosilicate) | 0.840 | Solid | 0.20× water |
| Iron / Steel | 0.449 | Solid metal | 0.11× water |
| Copper (Cu) | 0.385 | Solid metal | 0.09× water |
| Silver (Ag) | 0.235 | Solid metal | 0.056× water |
| Gold (Au) | 0.128 | Solid metal | 0.031× water |
| Lead (Pb) | 0.128 | Solid metal | 0.031× water |
Water's unusually high specific heat (4.186 J/g·°C) comes from its extensive hydrogen bonding network. Heating water requires not just speeding up molecular motion but also breaking and reforming hydrogen bonds between water molecules. A gram of water stores roughly 10× more thermal energy per degree than lead. This property makes water the coolant of choice for engines, reactors, and industrial processes, and explains why the ocean acts as Earth's thermal buffer — preventing extreme temperature swings that would make life impossible on land.
Worked Example: Heating Water for a Cup of Tea
How much energy does it take to heat 250 mL (250 g) of water from 15°C (tap water) to 100°C (boiling)?
Step 1: ΔT = 100 − 15 = 85°C
Step 2: q = m × c × ΔT = 250 × 4.186 × 85 = 88,957 J ≈ 89 kJ
Step 3: Convert to calories: 88,957 / 4.184 = 21,263 cal = 21.3 kcal
Step 4: A 1500W electric kettle does this in: 88,957 / 1500 = 59 seconds
Note: This only heats the water to 100°C. To evaporate it completely would require an additional 250 × 2,260 = 565,000 J = 565 kJ — over 6 times more energy!