Heat Capacity Calculator

Background.

Put 12,500 joules into a kilogram of water and its temperature rises by about 3 K. Put the same energy into a kilogram of copper and it climbs by about 32 K. The difference is heat capacity: how much energy something absorbs for each kelvin its temperature rises. It belongs to the whole object, not just the material, so a 150-litre bath has 600 times the heat capacity of a 250 mL cup filled from the same tap.

Measured, it is a ratio. Add a known amount of heat Q, record the temperature change ΔT, and C = Q ÷ ΔT in joules per kelvin. A kelvin and a degree Celsius are the same size of step, so a rise from 20 °C to 25 °C is a ΔT of 5 K and can be entered as 5 directly.

The everyday laboratory use is calibrating a calorimeter. Before an insulated vessel can measure the heat released by a reaction or a dissolving salt, you need to know how many joules it takes to warm the vessel and its contents by one kelvin. Running an electric heater of known power for a timed interval supplies a known Q, and the temperature rise then gives that calorimeter constant. Bomb calorimeters are usually calibrated the same way in principle, by burning a standard such as benzoic acid whose heat of combustion is known.

Dividing heat capacity by mass gives specific heat capacity, the material property listed in tables: about 4,180 J/(kg·K) for liquid water, roughly 900 for aluminium and 385 for copper. So one object-level figure can describe very different things; 2,500 J/K is about 0.6 kg of water or about 6.5 kg of copper.

The ratio assumes every joule stayed in the object and that nothing melted, boiled or reacted along the way.

What is heat capacity calculator?

Heat capacity C is the heat needed to change the temperature of a particular object by one kelvin, measured in joules per kelvin (J/K). Unlike specific heat capacity, which is per kilogram, it describes the whole object, so it doubles when the amount of material doubles. Measured over a finite temperature change, Q ÷ ΔT gives the average heat capacity across that interval; the IUPAC definition is the limit of the ratio as the temperature change shrinks toward zero.

How to use this calculator.

1. 01Enter the heat added or removed in Sensible heat magnitude, in joules. For an electric heater that is power in watts multiplied by time in seconds; 1 kJ is 1,000 J and a thermochemical kilocalorie is 4,184 J.
2. 02Enter the size of the temperature change in Temperature-change magnitude, in kelvin. A change measured in degrees Celsius is the same number; a change in degrees Fahrenheit must be multiplied by 5/9 first.
3. 03Count only heat that actually went into warming or cooling the object. If some of what you supplied escaped to the room, the true heat capacity is lower than the result.
4. 04Divide the answer by the object's mass in kilograms if you want specific heat capacity to compare with a data table.

The formula.

C = Q ÷ |ΔT|. Q is the sensible heat, the energy that changed the object's temperature without melting, boiling or reacting it, in joules. |ΔT| is the size of the temperature change in kelvin; heating and cooling give the same heat capacity, so only the magnitude matters. Joules divided by kelvin gives J/K, and since the formula is a single quotient, halving ΔT for the same heat doubles C. The answer is an average over the interval you measured. Near room temperature, solids and liquids change heat capacity only gradually, so a span of a few kelvin gives a value close to that at the midpoint, but heat capacity falls steeply at very low temperatures. For a gas it also matters whether the heat went in at constant pressure or constant volume, because Cp is larger than Cv.

A worked example.

Frequently asked questions.

References& sources.

1. [1]OpenStax, University Physics Volume 2, section 1.4, Heat Transfer, Specific Heat, and Calorimetry.
2. [2]IUPAC Gold Book, heat capacity.
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.