Specific heat of water: 4,186 J/(kg·K), which is 4.184 J/(g·°C) or 1 cal/(g·°C), what the number means, why water's is so high and what that does for the climate, the body and engines, the specific heat capacity table of 45 common substances (ice, steam, metals, air, oils, soils), the formula Q = mcΔT with worked examples, the latent heats, and a printable table

"Specific heat of water" is searched by students meeting Q = mcΔT for the first time, by anyone doing a calorimetry calculation, and by people who have read that water "holds heat well" and want the number. The number is 4,186 J/(kg·K), and the rest of this page is what it means, why it is so high, the table of other substances to compare it with, and the formula with worked examples of the kind set in grade 8 to 12 physics and chemistry. The printable has the table and the formula on one page and practice with answers on the other.

Download the specific heat capacity table and Q = mcΔT sheet (PDF) (the specific heat of 45 substances in J/(kg·K) and J/(g·°C), water's value in every unit, the formula with six worked examples, the latent heats, and ten practice questions with answers; two pages, free).

The number

The specific heat capacity of a substance is the energy needed to raise the temperature of one kilogram (or one gram) of it by one degree. Water needs 4,186 J for a kilogram and a degree. A kelvin and a degree Celsius are the same size of step, so J/(kg·K) and J/(kg·°C) are the same unit. The value drifts slightly with temperature (4,218 at 0 °C, 4,182 at 20 °C, 4,216 at 100 °C), which is why 4,186 and 4,184 and 4,200 all appear in books; use the one your course uses.

Why water's is so high

Temperature measures how fast molecules move. When heat goes into most substances it goes into motion, and the temperature rises. Water molecules are held to one another by hydrogen bonds, and part of any heat added is spent stretching and breaking those bonds instead of speeding the molecules up. So water absorbs a lot of energy for a small rise in temperature, and gives a lot back as it cools. Ice and steam have far fewer hydrogen bonds to work on, which is why their specific heats are about half of liquid water's.

What this does in the world:

• Climate: oceans warm and cool slowly, so coasts have milder summers and winters than inland places at the same latitude (San Francisco against Sacramento; Cornwall against the Midlands).
• The body: a body that is 60 percent water changes temperature slowly, which keeps the body's enzymes within their working range through a hot afternoon or a cold morning.
• Cooling and heating: water carries more heat per kilogram than any other cheap liquid, so it is the coolant in car engines and power stations and the working fluid in central heating and hot-water bottles.
• Cooking: a pan of water takes longer to heat than the same mass of oil (2,000 J/(kg·K)), and a boiling pot stays near 100 °C because the extra heat goes into the latent heat of steam.

The specific heat capacity table

Values are typical at room temperature; sources differ in the last digit or two.

The pattern: metals are low (a kilogram of copper warms ten times faster than a kilogram of water for the same heat), water and the light gases are high, and most rock, glass and soil sit around 800 to 900. Per atom, most solid elements are in fact similar (the Dulong-Petit rule, about 25 J/(mol·K)); the metals look low per kilogram only because their atoms are heavy.

The formula: Q = mcΔT

Q = m × c × ΔT

• Q: heat energy transferred, in joules
• m: mass, in kg (or grams, if c is per gram)
• c: specific heat capacity, in J/(kg·K)
• ΔT: the change in temperature, final minus initial, in K or °C

Rearranged: c = Q ÷ (mΔT) to find a specific heat from a measurement, ΔT = Q ÷ (mc) to find how much something warms, m = Q ÷ (cΔT) to find a mass.

Watch the units: if the mass is in grams, use c in J/(g·°C) (4.18 for water) or convert the grams to kilograms first. A temperature change is the same in kelvin and in Celsius, so no conversion is needed for ΔT.

Latent heat: the energy that does not change the temperature

Melting ice and boiling water take energy with no rise in temperature, because the energy goes into breaking the structure, not into speed:

So turning 1 kg of ice at 0 °C into steam at 100 °C takes 334 kJ (melt) + 419 kJ (warm 100 °C) + 2,260 kJ (boil) = about 3,013 kJ, and the boiling step is three quarters of it. This is why steam burns are worse than boiling-water burns and why sweating cools: each gram of sweat that evaporates takes about 2,260 J from the skin.

Where it sits in school

Specific heat capacity and Q = mcΔT are grade 8 and 9 physical science in the United States (and chemistry's calorimetry in grade 10 and 11, with the calorie and 4.184 J/(g·°C)); GCSE Physics (Energy, with the required practical measuring c for a metal block) and A level in England; Year 9 and 10 science and Year 11 Physics in Australia; CBSE Class 9 (Matter in Our Surroundings, latent heat) and Class 11 Physics (Thermal Properties). The common mistakes: mixing grams with J/(kg·K), using the final temperature instead of the change, and forgetting that the latent heat steps have ΔT = 0.

Practice: ten questions

1. How much energy warms 1.5 kg of water from 15 °C to 65 °C?
2. How much energy warms 1.5 kg of aluminium by the same 50 °C?
3. 500 J goes into 100 g of water. By how much does its temperature rise?
4. 500 J goes into 100 g of gold. By how much does its temperature rise?
5. A 2 kg steel block (c = 490) cools from 300 °C to 20 °C. How much heat does it give out?
6. A substance of mass 0.4 kg warms 25 °C when given 12,900 J. What is its specific heat, and what might it be?
7. A 3 kW kettle holds 1.2 kg of water at 18 °C. How long to reach 100 °C (ignore losses)?
8. How much energy melts 0.5 kg of ice at 0 °C?
9. How much energy turns 0.5 kg of water at 100 °C into steam?
10. Why does a beach's sand get hotter than the sea on a sunny afternoon?

Answers: 1) 1.5 × 4,186 × 50 = 313,950 J (314 kJ). 2) 1.5 × 900 × 50 = 67,500 J. 3) 500 ÷ (0.1 × 4,186) = 1.2 °C. 4) 500 ÷ (0.1 × 129) = 38.8 °C. 5) 2 × 490 × 280 = 274,400 J. 6) 12,900 ÷ (0.4 × 25) = 1,290 J/(kg·K): about polystyrene or paper. 7) Q = 1.2 × 4,186 × 82 = 411,906 J; ÷ 3,000 W = 137 s, about 2 min 17 s. 8) 0.5 × 334,000 = 167,000 J. 9) 0.5 × 2,260,000 = 1,130,000 J. 10) Sand's specific heat (830) is a fifth of water's (4,186), so the same sunshine raises its temperature about five times as much, and the sea also mixes and evaporates.

Download the specific heat capacity table and Q = mcΔT sheet (PDF)

Where to get help

A 1-on-1 online physics or chemistry class with a tutor who holds a master's degree in science, for grades 8 to 12 in the US curriculum, GCSE and A level, the Australian years and CBSE: Q = mcΔT worked on the shared screen with the units written on every line, the latent-heat steps drawn on a heating curve, then the exam questions. The recording and notes after every class, the same tutor every week, US$10 to $13 an hour. The physics page has the courses; the free 30-minute first class is a real lesson, usually on the homework the student brings.

Questions parents ask

See how we teach this, 1-on-1 online →