How this instrument works
Specific heat capacity, written c, is a substance's toll for warming up: joules needed per kilogram per kelvin. Joseph Black prised it apart from temperature at Glasgow in the 1760s, after noticing that equal masses of different materials, set over identical flames, climb at wildly different rates. Water charges 4186 J/kg·K. Copper charges 385, lead only 128. That gap explains why lead sinkers snatched off hot stoves sting your fingers just briefly, while mugs of tea stay dangerous for several minutes.
Water's figure is an outlier among ordinary liquids, one consequence of hydrogen bonds absorbing energy as they stretch and reshuffle rather than simply hurrying molecules along. Coastal towns owe mild winters to it, engine coolant owes its whole job to it, and nutrition labels quietly depend on it: one dietary Calorie is a kilocalorie, once defined as enough heat to lift a kilogram of water by one degree. Solids sit far lower, and Dulong and Petit noticed in 1819 that most solid elements cluster near 25 joules per mole per kelvin whatever their identity — regularity that quantum theory later explained, and which collapses at cryogenic temperatures where c falls toward zero.
Q = m·c·ΔT assumes c holds steady across your interval and that nothing melts, boils or freezes en route. Both assumptions break routinely. Water's c drifts by roughly one percent between 0 °C and 100 °C, so precise work quotes a temperature alongside every tabulated value. Gases need a stated condition, since heating at constant pressure costs more than at constant volume: expansion does work on whatever surrounds it. Cross a phase boundary and this equation stops short — melting ice at 0 °C swallows 334 kJ/kg with ΔT pinned at zero, so latent heat belongs on its own line of any energy budget.
- Type your sample size into Mass — grams, kilograms, tonnes or pounds all work from that field's unit menu.
- Put your material's constant into Specific heat capacity (J/kg·K): 4186 for water, 900 for aluminium, 450 for steel, 385 for copper.
- Enter Temperature change (K or °C) as a difference, never an absolute reading — a climb from 18 °C to 62 °C is 44, not 62.
- Read Heat energy, switching its units between joules, kilojoules, calories, kilocalories or watt-hours to suit your apparatus.
- For cooling, make Temperature change negative; Heat energy comes back negative too, meaning energy leaving your sample.
Worked example — one litre of water, one degree warmer
A beaker holds one litre of water, 1 kg on your balance, and you want it exactly one kelvin warmer: 19.5 °C becoming 20.5 °C. Mass = 1, Specific heat capacity = 4186, Temperature change = 1. Multiply straight through: Q = 1 × 4186 × 1 = 4186 J.
That figure is no accident. It is where a calorie came from, back when heat was gauged by what water did rather than by joules — 4186 J is one kilocalorie, and matches water measured near 15 °C. Read another way, 4186 J is 1.16 watt-hours, so a 100 W immersion heater needs about 42 seconds, assuming nothing leaks into glass, bench or room air. Real kettles leak plenty, which is why measured timings always run long.
Questions
Is J/kg·K identical to J/kg·°C?
Yes, exactly. Kelvins and Celsius degrees are equal in size; only their zero points differ, and taking a difference erases any offset. So water is 4186 J/kg·K and 4186 J/kg·°C with no conversion between them. Imperial tables are where care is needed: water reads 1 BTU/lb·°F by construction, which is the same physical quantity wearing different clothes.
What if my sample melts or boils partway through?
Split your calculation into stages. Q = m·c·ΔT covers warming inside a single phase only. Taking ice at −10 °C up to water at 20 °C needs three terms: warm ice (c ≈ 2090) to 0 °C, melt it (334,000 J/kg, with no temperature change at all), then warm liquid water (c = 4186) to 20 °C. Omitting that middle term throws away three quarters of your energy bill, and it is by far the commonest error with this formula.
Why is my answer coming out negative?
Because Temperature change was entered as a negative number, which describes cooling. Q then counts energy leaving your sample rather than entering it. Sign follows straight from ΔT = T_final − T_initial: coffee falling from 80 °C to 20 °C gives ΔT = −60 and negative Q. Magnitude is what sizes your radiator or chiller; sign only records which direction energy travels.
Which value should I use for a gas?
Whichever matches how your gas is confined. Heating at constant pressure lets it expand and push against its surroundings, so cp always exceeds cv — dry air runs about 1005 J/kg·K at constant pressure but 718 at constant volume, some 40 percent apart and far too wide to guess at. Ducts, vents and open vessels take cp; a sealed rigid cylinder takes cv. Liquids and solids barely expand, so published values for them are effectively cp and you can ignore this distinction.
How does specific heat differ from heat capacity?
Heat capacity C is extensive, measured in J/K, and belongs to one particular object: your kettle, your calorimeter, that copper block on your bench. Specific heat c is intensive, measured in J/kg·K, and belongs to a material however much of it you happen to hold. They join through C = m·c. Chemists carry a third cousin, molar heat capacity in J/mol·K, which is what Dulong and Petit's near-constant 25 refers to.
Where do published c values actually come from?
From calorimetry: a measured energy input, usually electrical, delivered into a well-insulated sample whose temperature rise is tracked closely, corrected for whatever heat an apparatus absorbs on its own account. Laboratories now lean on differential scanning calorimetry, comparing a sample against a reference as both ramp through a programmed temperature sweep. Every tabulated value carries a temperature with it, because c is a mild function of temperature — water sits at 4217 J/kg·K near freezing and dips to about 4178 around 35 °C.