Specific heat and heat capacity: four quantities with similar names

Q = mcΔT, with the three quantities students mix up kept apart: specific heat capacity per kilogram, heat capacity for the whole object, molar heat capacity per mole, and the water equivalent in grams — plus how long a heater of a given power will take.

Last updated 11 Nov 2026

Heat required, and the four capacities

Q = mcΔT, with the heater time beside it

Mass being heated or cooledIn kilograms. For water you can read litres as kilograms to a quarter of a per cent over the whole liquid range, which is well inside the error in anything else on this page.

Specific heat capacityFive values, each with a document behind it. Water is listed three times on purpose: NCERT’s own module prints 4186 in its text and 4.2 × 10³ in one of its own examples, and the measured value is 4181.6 at 25 °C, rising to 4220 at 0 and 4216 at 100. Aluminium, iron, brass, lead and glass are deliberately absent. The figures everyone quotes (900, 450, 380, 130, 840) are in a thousand places and this page could trace none of them to a published source, so it asks you for the one in your question instead of printing them with a confident air. Choose the last option and the box below unlocks.

Specific heat capacity, typed inLocked while a value is selected above. Pick the last option up there and this becomes the input, which is how aluminium, brass, ethanol or anything else your question names still works. The arithmetic does not care where the number came from — the UNIT does. This field wants J kg⁻¹ K⁻¹: a table in J g⁻¹ K⁻¹ needs ×1000, one in cal g⁻¹ °C⁻¹ needs ×4186. Entering 0.39 for copper instead of 390 is the commonest way a calorimetry answer comes out a thousand times wrong.

Temperature changeA change, not a temperature: the number of degrees, which is the same figure in Celsius and in kelvin. Heating water from 20 °C to 100 °C is 80, not 373. Putting an absolute temperature in here is the single commonest error on this calculation and it inflates the answer by about 4.4 times for that example. Negative is allowed and means cooling, which makes Q negative: heat leaving rather than arriving.

Power of the heaterIn watts, and it is here because it turns an abstract energy into something you can time with a clock. A watt is a joule per second, so the time rows below are simply Q divided by this. Assumes every joule reaches the substance: a real kettle loses heat to its body and to the room, so the measured time is always longer than the calculated one, never shorter. If yours is shorter, something is wrong with the mass or the specific heat.

502,320JExample

1.5 kg of water taken from 20 °C to 100 °C by a 2000 W kettle, on NCERT’s 4186 J/kg/K

One equation, four capacities, and only one of them is per kilogram

Q = m c ΔT · C = m c · C_molar = c M · water equivalent = m c / c_water · t = Q / P

c: specific heat capacity: joules per kilogram per kelvin, a property of the SUBSTANCE and nothing else. Water’s 4186 is unusually large, which is why water is the coolant of choice and why the sea moderates a coastal climate
C = mc: heat capacity (sometimes thermal capacity): joules per kelvin, a property of the OBJECT. This is the one that does the work in a calorimetry question, and the distinction from c is the commonest confusion on the topic. A bath and a teaspoon of the same water have the same c and wildly different C
C_molar = cM: molar heat capacity: joules per mole per kelvin, which is where the topic becomes interesting. Multiply the specific heat by the molar mass in kg mol⁻¹. For most simple solids it comes out near 25 J mol⁻¹ K⁻¹ whatever the metal, which is a fact about atoms rather than about materials; per kilogram the same metals look entirely different
ΔT: a temperature DIFFERENCE, identical in Celsius and kelvin. Using an absolute temperature here instead of the change is the error this page prints a row for, so you can see what it would have cost
t = Q/P: the time a heater of power P needs, since a watt is a joule per second. The calculation always UNDERSTATES a real time, never overstates it, because real heaters lose energy to everything that is not the substance

Worked example

1.5 kg of water taken from 20 °C to 100 °C by a 2000 W kettle, on NCERT's 4186 J/kg/K
THE TEMPERATURE CHANGE, which is where this goes wrong. From 20 °C to 100 °C is ΔT = 80 K, not 373 and not 393. In kelvin the same change is 293.15 K to 373.15 K, and the difference is still 80, which is the point: ΔT is scale-independent
Q = m c ΔT = 1.5 × 4186 × 80 = 502 320 J, which is 502.3 kJ or 0.1395 kWh. For comparison the page also prints what the absolute temperature would have given: 1.5 × 4186 × 353.15 = 2.218 MJ, which is 4.4 times too large — the mistake is not subtle in its consequences, only in its appearance
THE HEAT CAPACITY OF THIS KETTLEFUL. C = m c = 1.5 × 4186 = 6279 J K⁻¹. That is the number to carry if the same water is going to appear in a mixture problem, and its water equivalent is 1500 g — trivially, because it IS water
THE TIME, which is the row worth sanity-checking against life. t = Q/P = 502 320 / 2000 = 251.2 s, about 4 minutes 11 seconds, and the kettle rises at 2000/6279 = 0.319 K per second, or 19.1 K a minute. A real 2 kW kettle with 1.5 litres in it takes rather longer than four minutes, and the gap is the heat that went into the kettle body, the element and the kitchen. The calculation is a lower bound on the time and an upper bound on the efficiency
THE MOLAR FIGURE, for the sake of the comparison. Water's molar mass is 18.02 g mol⁻¹, so C_molar = 4186 × 0.018 02 = 75.4 J mol⁻¹ K⁻¹, and 1.5 kg is 83.2 mol. Copper's molar figure is 24.8 on the same arithmetic. Per kilogram the two substances differ by a factor of eleven; per mole, by three

The same metals ranked two ways: per kilogram and per mole

Five sourced values, and the fourth column is the reason the table is here. Copper’s specific heat is a tenth of water’s and looks like a different kind of quantity; per mole the two are within a factor of three, and copper’s 24.8 J mol⁻¹ K⁻¹ sits almost exactly on the value that most simple crystalline solids share at room temperature. The molar figures are this page’s own arithmetic, c × M, not quoted values. Note that ice and liquid water have the same molar mass and half the heat capacity: the molecules are the same, and what changed is how freely they can move and therefore how many ways they have of storing the energy. Aluminium, iron, brass, lead and glass are absent from the table for the same reason they are absent from the dropdown — the figures everyone quotes could not be traced to a source for this batch, and a sourced short list is worth more than a long unsourced one.
Substance	Specific heat c (J/kg/K)	Molar mass (g/mol)	Molar heat capacity (J/mol/K)	Source of the specific heat
Water	4186	18.02	75.4	NCERT CIET module, text
Water	4200	18.02	75.7	NCERT CIET module, worked example
Water, measured at 25 °C	4181.6	18.02	75.3	Engineering ToolBox
Ice (below 0 °C)	2100	18.02	37.8	NCERT CIET module
Copper	390	63.55	24.8	NCERT CIET module, 0.39 J/g/K

Why four quantities share one idea, and which one your question wants

Specific heat capacity is per kilogram, heat capacity is per object, molar heat capacity is per mole, and a water equivalent is a mass in grams. All four describe the same physical idea — how much energy a degree costs — and questions move between them without warning. The one that goes in Q = mcΔT is the first. The one that goes into a calorimetry sum is the second, because what matters when two bodies mix is each body’s total m·c and not its material. The third is where the physics is. The fourth is a laboratory convenience that lets you fold a copper can into a mass of water.

The commonest error on this page is putting a temperature where a temperature change belongs, so the page prints what that would have given as a row of its own. Heating 1.5 kg of water from 20 °C to 100 °C needs 502 kJ; the same calculation done with 353.15 K instead of 80 K gives 2.22 MJ, 4.4 times too much. There is no scale argument that rescues it: ΔT is a difference and is the same number in Celsius and kelvin, which is exactly why no conversion is needed and why the mistake survives a units check. The second commonest is the specific heat’s own unit — 0.39 against 390 for copper — and the third is forgetting that the whole formula assumes no change of state.

The molar column is the one worth looking at twice. Per kilogram, water at 4186 and copper at 390 look like different kinds of substance. Per mole they are 75.4 and 24.8 J mol⁻¹ K⁻¹, and copper’s figure is one that most simple crystalline solids share at room temperature, give or take, whatever the metal. That is a statement about atoms rather than about materials: a mole of any of them has the same number of atoms, each with the same small number of ways to store energy, so each costs about the same per degree. Per kilogram they differ wildly only because a mole of lead weighs thirty times what a mole of beryllium does. Reading the table both ways is the quickest way to see that specific heat is mostly a fact about molar mass.

Why water’s value is so large, and why it is not actually constant. 4186 J kg⁻¹ K⁻¹ is several times most solids and about four times air, which is why water is the coolant in a car and in a power station, why a hot water bottle beats a warm brick, and why the sea keeps a coast mild. It also is not one number: the measured isobaric value dips to a minimum of about 4179.6 near 40 °C and rises at both ends of the liquid range, 4219.9 at 0 °C and 4215.7 at 100, a spread of about 0.96 per cent. School tables quote one figure and NCERT’s own module quotes two of them, 4186 and 4.2 × 10³, in the same document. This page offers all three sourced values and asks you to pick, because the one your marking scheme used is the one that gets the last significant figure right.

And the heater power row, which is there to make the joule mean something. A joule is small and a kilojoule is abstract, but 4 minutes 11 seconds on a 2 kW kettle is checkable in a kitchen. The calculation assumes every joule reaches the water, so the real time is always longer — the difference being everything that went into the kettle body, the element and the room. That makes it a lower bound on the time and an upper bound on the efficiency, which is the right way round for a sanity check: if a measured time comes out SHORTER than this calculation, the mass or the specific heat is wrong, because nothing can heat faster than perfectly.

Frequently asked questions

What is the difference between specific heat capacity and heat capacity?

Specific heat capacity c is per kilogram and belongs to the substance; heat capacity C = mc is for the whole object and belongs to the object. Water in a bath and water in a teaspoon have the same specific heat capacity and wildly different heat capacities. The units give it away: J kg⁻¹ K⁻¹ against J K⁻¹. Q = mcΔT wants the first; a calorimetry mixture wants the second, which is why the final temperature of a mixture depends on the two m·c products and not on the two specific heats.

Do I use Celsius or kelvin for the temperature change?

Either, because they give the same number. The degree Celsius is defined as equal in magnitude to the kelvin, so a change of 80 °C is a change of exactly 80 K. What you must NOT do is use a temperature in place of a change. If a question gives two temperatures, subtract them first; if it gives one temperature and no second one, it is probably not a Q = mcΔT question at all.

Why does my kettle take longer than this page says?

Because the calculation gives the energy that ends up in the water and the kettle also has to heat its own body, its element and a little of the kitchen, and loses heat from its surface the whole time it is on. This page does not put a figure on that loss, because no sourced one was available for it; what it can say is that the shortfall is worse on a small volume, where the fixed cost of warming the kettle itself is a larger share of the total. The useful consequence is the direction: this figure is always a lower bound on the time, so a measured time that is shorter means an input is wrong rather than that your kettle beat physics.

Why do nearly all metals have a molar heat capacity near 25 J/mol/K?

Because a mole of any solid element contains the same number of atoms, each held in place by its neighbours with a similar small number of ways to store energy, so each atom costs about the same to warm by a degree. Copper’s 24.8 on this page’s arithmetic is a typical figure. Per kilogram the same metals look completely different, and the whole difference is molar mass — which is why specific heat capacity, the quantity school questions use, is largely a fact about how heavy the atoms are rather than about the material’s character. The rule weakens at low temperatures and for light, stiff solids, where it fails badly.

Can I use this for a substance that melts or boils on the way?

No, and that is the one limit of the formula worth memorising. Q = mcΔT is sensible heat only; it assumes the substance changes temperature and nothing else. Crossing a melting or boiling point needs a latent-heat term at constant temperature, and that term is usually the biggest of the lot: melting a kilogram of ice takes 333 000 J, as much as warming that kilogram of water by eighty degrees, and boiling it takes 2 260 000 J. The latent-heat page does the three-term version.

Related calculators

References

NCERT / CIET, Physics-02 (Keph_201104): Thermal Properties of Matter, Unit 7 Module 15, “Change of State” (chapter 11, class XI), 2019, on the Central Institute of Educational Technology e-content server (read 11 November 2026). The source of every material constant this batch prints without hedging: ice 2100 J kg⁻¹ K⁻¹, water 4186 — written 4.2 × 10³ in a different worked example in the same module — copper 0.39 J g⁻¹ K⁻¹, latent heat of fusion 3.33 × 10⁵ J kg⁻¹ in the text against 3.35 × 10⁵ and 335 J g⁻¹ in its own examples, and latent heat of vaporisation 22.6 × 10⁵ in the text against 2.256 × 10⁶ in an example. Those are not misprints to tidy away: one official module gives the same quantity two ways, 0.6 per cent apart on fusion and 0.18 per cent apart on vaporisation. That is why this batch takes the constant from the reader instead of choosing one for them.
Specific Heat Capacity of Water: Temperature-Dependent Data and Calculator, The Engineering ToolBox (2004) (read 11 November 2026). The source of the 4181.6 J kg⁻¹ K⁻¹ option here and of the curve behind it: at saturation pressure the isobaric specific heat runs 4.2199 kJ kg⁻¹ K⁻¹ at 0.01 °C, 4.1955 at 10, 4.1844 at 20, 4.1816 at 25, a minimum of 4.1796 at 40, then back up through 4.1851 at 60, 4.1969 at 80 and 4.2157 at 100. Water’s specific heat is a shallow U with its floor near 40 °C, and the 0.96 per cent spread across the liquid range is wider than the gap between the two NCERT figures. The page states that it names no primary source of its own, which is why these figures sit beside the NCERT ones rather than replacing them.
The International System of Units (SI), 9th edition, BIPM, published May 2019; the version read for this batch is 4.01, revised June 2026 (read 11 November 2026). The source of the kelvin’s CURRENT definition: the kelvin is defined by fixing the Boltzmann constant at exactly k = 1.380 649 × 10⁻²³ kg m² s⁻² K⁻¹, which the brochure states as an exact relation. The degree Celsius is defined equal in magnitude to the kelvin, with T₀ = 273.15 K and t/°C = T/K − 273.15. Most school textbooks still define the kelvin as 1/273.16 of the triple point of water. The brochure records that as the PREVIOUS definition, and says the triple-point temperature must now be determined experimentally — it stood at 273.16 K with a relative standard uncertainty of 3.7 × 10⁻⁷ at the redefinition, and is a measured quantity from then on.
COULD NOT BE READ, and nothing was substituted for any of it. The NCERT textbook pages on ncert.nic.in, and four CIET modules in the same series as the ones cited here — Keph_201101 (temperature and its measurement), Keph_201102 (thermal expansion), Keph_201103 (specific heat capacity and calorimetry) and Keph_201105 (conduction and convection) — were all refused by the server’s robots policy on 11 November 2026. That is why this batch quotes no NCERT table number, and why the coefficients of expansion and the thermal conductivities are attributed to the reference actually read rather than to the textbook table you are more likely to be holding. If your table disagrees, use your table: these pages take the constant from you for exactly that reason.