Specific heat is the energy it takes to warm one kilogram of a substance by one degree, and for water the usual classroom figure is 4200 J/(kg·K). NIST's reference values for liquid water at sea-level pressure run from about 4179 J/(kg·K), lowest in the mid-30s °C, to 4219 J/(kg·K) just above freezing. We recomputed eight everyday heating cases from that data, and 4200 overstated the heat in every one, by 0.22% to 0.50%. Measuring hot water by the litre and calling it kilograms moved the answer further: 4.3% at boiling.
A single classroom figure understates water's specific heat near freezing and boiling
The values come from the NIST Chemistry WebBook's fluid data for water at 0.101325 MPa, queried on 4 November 2026. They are computed from the IAPWS-95 equation of state (Wagner and Pruss, 2002), a fit to many measurements, and NIST gives their uncertainty as "0.1% in the liquid".
From 0 to 100 °C the curve is a shallow U. It starts at 4219.4 J/(kg·K) at 0.01 °C, falls to about 4179 somewhere in the mid-30s, and climbs back to 4215.6 in liquid water at the boiling point. The highest is 0.96% above the lowest. The shape is standard reference data; we did not discover it.
Reading NIST's values at half-degree steps, we found the curve crosses 4200 at 7.3 °C and again at 84.1 °C. Outside those two points 4200 is too low; between them, too high.
Calling a calorie the heat for a gram of water overstates its precision
NIST's Special Publication 811, its guide to SI units, lists five calories in its Appendix B.8:
- the thermochemical calorie, 4.184 J exactly;
- the International Table calorie, 4.1868 J;
- the mean calorie, 4.190 02 J;
- the 15 °C calorie, 4.185 80 J;
- the 20 °C calorie, 4.181 90 J.
The largest is 0.19% above the smallest. The table also gives the plain symbol "cal" to the mean calorie, so a line reading "1 cal = 4.184 J" is naming the thermochemical calorie without saying so. SP 811's footnotes date the International Table calorie to a 1956 steam conference in London, and say the gram calorie only "approximates" the energy that warms a gram of water by a degree.
On our arithmetic, the 15 °C calorie sits 0.06% below NIST's current value at 15.01 °C (4188.4 J/(kg·K)), and the 20 °C calorie 0.05% below the value at 20.01 °C (4184.0). We found no source explaining the gap. The food Calorie is a kilocalorie, and SP 811 calls "large calorie" an obsolete name for it; our guide to macros covers the nutrition side.
The classroom value overstates a kettle's heat by a quarter of a percent
For each case we took the true heat from NIST's enthalpy values at eight digits and turned volumes into mass with NIST's density at the starting temperature. All cases are liquid water at one atmosphere with no losses, and the kettle row counts only heat into the water. The true-heat column is our calculation; the last three columns are the error from each fixed value.
| Case | True heat (J, ours) | 4200 | 4186 | 4184 |
|---|---|---|---|---|
| 1 L, 25 °C to boiling | 313,210 | +0.24% | −0.09% | −0.14% |
| 1 L, 4 to 25 °C | 88,004 | +0.22% | −0.11% | −0.16% |
| 250 mL, 25 to 80 °C | 57,364 | +0.38% | +0.04% | −0.01% |
| 0.5 L, 0.01 to 37 °C | 77,475 | +0.25% | −0.09% | −0.13% |
| 150 L, 30 to 40 °C | 6,241,792 | +0.49% | +0.16% | +0.11% |
| 2.0 kg, 20 to 25 °C | 41,826 | +0.42% | +0.08% | +0.03% |
| 1 kg, 14.5 to 15.5 °C | 4,188 | +0.28% | −0.06% | −0.11% |
| 1 kg, 34.5 to 35.5 °C | 4,179 | +0.50% | +0.16% | +0.11% |
A litre at 25 °C is 0.9970 kg, and boiling it takes 313,210 J; 4200 gives 0.24% more. Across the eight cases 4200 ran 0.22% to 0.50% high, two to five times NIST's stated uncertainty.
The other two constants landed within −0.16% and +0.16%, spreads about the size of the uncertainty itself, so this data cannot rank either as the better choice. Each matches NIST twice: 4184 at 20.1 °C and 57.7 °C, and 4186 at 17.5 °C and 62.3 °C.
Solving backwards with 4200 understates the temperature rise and the mass
Run Q = mcΔT backwards and the error flips sign. Give our heat transfer calculator the kettle's true heat (Q = 313210 J), m = 0.997 kg and c = 4200 J/(kg·K), and it solves ΔT as 74.8 K (unrounded 74.7982041 K) against a real rise of 74.97 K. Asked for the mass with ΔT = 74.97 K, it returns 0.9947 kg against the true 0.9970. Over the eight cases, a ΔT or mass solved with 4200 comes out 0.22% to 0.49% low.
Forwards, m = 0.997 kg, ΔT = 75.0 K and c = 4190 J/(kg·K) give a headline of 3.13 × 10⁵ J, rounded to three significant figures and 0.07% below our figure, with 3.1330725 × 10⁵ J unrounded beside it.
Until 4 November 2026 the calculator showed a typed 4200 as 4000, solved heat in with a falling temperature to a mass of −2 kg, described a conduction method it never ran, and called 4.184 J the heat that warms a gram of water by a degree. The revision that day fixed all four.
Counting a litre as a kilogram exaggerates hot water's mass by up to 4.3%
Water expands as it warms. From NIST's densities, we worked out that treating a litre as a kilogram overstates the mass by 0.30% for water measured at 25 °C, about the size of the whole 4200 error.
The error grows if the water is measured when hot, reaching 2.9% at 80 °C and 4.3% at boiling, where NIST puts the density at about 958 kg/m³. Water measured cold and then heated keeps its original mass.
Rounded inputs misstate the answer more than any choice of constant
Type m = 1, ΔT = 75 and c = 4200 into the calculator and the headline is 3 × 10⁵ J, labelled as rounded to one significant figure, with 3.15 × 10⁵ J unrounded beside it. That headline is 4.22% below our kettle figure, about 17 times the 0.24% that 4200 introduces in the same case.
Typing 1.0 kg instead gives 3.2 × 10⁵ J, 2.17% high. With 1.00 kg and 75.0 K it is 3.15 × 10⁵ J, 0.57% high. Our guide to the digits your calculator invents covers why.
Cambridge's IGCSE syllabus leaves water's specific heat unstated
The Cambridge IGCSE Physics 0625 syllabus for exams in 2026 to 2028 puts specific heat capacity in its Supplement content, section 2.2.2, beyond the core. There students recall and use c = ΔE/(mΔθ), printed as a fraction. The core asks only that a temperature rise increases internal energy.
We searched its text for 4200, 4.2 and every mention of water: it states no value for water's specific heat. We did not open past papers, so cannot say what any exam supplies. Its symbols table gives the unit as J/(g °C) or J/(kg °C). In the gram form, water's reference values run from about 4.18 to 4.22, a range the thermochemical calorie's 4.184 sits inside.
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