Specific Heat Calculator

Water's specific heat — about 4.184 J/(g·°C) or 4184 J/(kg·K) — is among the highest of any common liquid because of hydrogen bonding. Each H2O molecule can form up to four hydrogen bonds with neighbors. When you add heat to liquid water, much of the energy goes into stretching and breaking those hydrogen bonds rather than directly increasing molecular kinetic energy, so the temperature rises only slowly per joule supplied. For comparison (J/g·°C): water 4.18; ethanol 2.44; aluminum 0.90; iron 0.45; copper 0.39; gold 0.13. Water's value is about ten times that of typical metals. This is why oceans buffer coastal climates against day-night swings, why a 70-kg human (about 60% water) can absorb a lot of metabolic heat without overheating, and why water-glycol mixtures are used as engine coolants. Calculation: heating 1 kg of water from 20 °C to 100 °C takes Q = m c ΔT = 1.0 × 4184 × 80 = 335 kJ.

Not for ordinary substances at ordinary conditions. The textbook definition c = Q / (m ΔT) yields a positive number whenever heat input raises temperature, which is the normal case. Apparent exceptions: (1) During a phase change (melting, boiling), heat is absorbed but temperature is constant, so c is undefined for that interval — use latent heat instead. (2) Self-gravitating astrophysical systems (stars, star clusters) can show negative heat capacity: a star that radiates energy contracts, converting gravitational potential energy into kinetic energy of its particles, so its temperature rises while it loses heat. (3) Black holes have negative heat capacity in the Hawking-Bekenstein framework. (4) Sign-convention slips — confusing Q absorbed by the system vs Q released to surroundings — sometimes produce a negative number that is just a labeling issue. For introductory chemistry calculations, treat specific heat as a positive material constant; if your answer comes out negative, check the sign of Q and the order of (Tfinal - Tinitial).

Apply conservation of energy: heat lost by the hotter substance equals heat gained by the cooler one. Mixing two substances with no phase change: m1 c1 (T1 - Tf) = m2 c2 (Tf - T2), which solves to Tf = (m1 c1 T1 + m2 c2 T2) / (m1 c1 + m2 c2). Example: 100 g of water at 80 °C mixed with 200 g of water at 20 °C → Tf = (100 × 80 + 200 × 20) / (100 + 200) = 40 °C (the c terms cancel). Heat added or removed from a single substance: Tf = Ti + Q / (m c). Example: 500 g of water at 25 °C absorbs 5000 J → ΔT = 5000 / (500 × 4.184) = 2.39 °C, so Tf = 27.4 °C. If a phase change is involved, account for latent heat. For ice at 0 °C melting into water, add m × Lf with Lf = 334 J/g before the warming term. Sanity check: the final temperature must lie between the initial temperatures of the two substances.

Both describe how much heat changes temperature, but at different scales. Heat capacity (C, in J/K or J/°C) is for a specific object: C = Q / ΔT. It depends on both the material and the amount. A 500 g aluminum block has C = 500 × 0.90 = 450 J/K. Specific heat capacity (c, in J/(g·K) or J/(g·°C)) is per gram: c = Q / (m ΔT). It is a material property and is independent of the sample size. Water always has c = 4.184 J/(g·°C). Relationship: C = m × c, so the heat capacity of any object equals its mass times the specific heat of the material. Heat capacity is extensive (doubles when mass doubles); specific heat is intensive (does not). Molar heat capacity, Cm = M × c, is the heat per mole and is the form usually tabulated for gases.

Approximately 1.005 J/(g·°C) at constant pressure (cp) or 0.718 J/(g·°C) at constant volume (cv) at room temperature. For an ideal gas the difference cp - cv equals R, the specific gas constant. For air, R ≈ 287 J/(kg·K), so cp - cv = 0.287 J/(g·K). The ratio cp/cv = γ ≈ 1.40 for diatomic gases and is what shows up in adiabatic-process equations. Compared with liquids (water 4.18 J/(g·°C), ethanol 2.44) and metals (iron 0.45, copper 0.39), air is on the low end — which is why a desert can swing 25 °C between day and night while a coastline buffered by water rarely swings more than a few degrees. Worked example: heating 1 m^3 of air at 25 °C from 20 to 30 °C. Air density ≈ 1.18 kg/m^3, so m = 1.18 kg; Q = 1.18 × 1005 × 10 ≈ 11.9 kJ.

Approximately 0.235 J/(g·°C), or 235 J/(kg·K). Silver has one of the lower specific heats among common metals. For comparison (J/(g·°C)): Al 0.90; Fe 0.45; Cu 0.39; Zn 0.38; Ag 0.235; Au 0.13; Pb 0.13. Heavier metals tend to have lower specific heats per gram because their molar heat capacities are nearly constant near room temperature (Dulong-Petit: about 25 J/(mol·K) for most monatomic solids), so heavier atoms mean fewer atoms per gram. For silver: 25 / 107.87 ≈ 0.232 J/(g·°C), close to the measured 0.235. Worked example: heating a 100 g silver bar from 20 °C to 100 °C requires Q = 100 × 0.235 × 80 = 1.88 kJ. Heating the same mass of water through the same range needs 33.4 kJ — almost 18× more. Practical implication: silver heats and cools quickly, which is why it is used in heat-sink and conductive-paste applications.