Hong Life CalculatorsUnderstanding the specific heat converter — concept and principle
This converter changes specific heat capacity between J/(kg·K), kJ/(kg·K), cal/(g·°C) and BTU/(lb·°F). Specific heat tells you how much energy it takes to warm one unit of mass of a material by one degree. Engineers, students and cooks use it to size heaters, compare materials, or read older tables written in calories or British thermal units.
How it is calculated
The value is converted to J/(kg·K) and then divided by the size of the target unit. The factors, using International Table (IT) calories and BTUs, are exact:
- 1 kJ/(kg·K) = 1,000 J/(kg·K).
- 1 cal/(g·°C) = 4,186.8 J/(kg·K), because 1 cal(IT) = 4.1868 J and 1 g = 0.001 kg.
- 1 BTU/(lb·°F) = 4,186.8 J/(kg·K).
A temperature difference of 1 °C equals 1 K, so the °C and K in these units are interchangeable.
The principle
Heat needed to change temperature follows Q = m × c × ΔT, where m is the mass, c the specific heat and ΔT the temperature change. The unit of c is therefore energy ÷ (mass × temperature difference). The calorie and the BTU were both defined historically as the heat that warms a unit of water by one degree: one gram by 1 °C, or one pound by 1 °F. Because both are anchored to water, water's specific heat is about 1 in either unit, and the IT definitions were chosen so that 1 cal/(g·°C) and 1 BTU/(lb·°F) are exactly equal. The thermochemical calorie (4.184 J) is a slightly different unit and would give 4,184 J/(kg·K).
Worked example
Default inputs: 1 cal/(g·°C) (IT) converted to J/(kg·K).
- 1 cal(IT) = 4.1868 J, so 1 cal/g = 4.1868 J/g.
- Per kilogram: 4.1868 J/g × 1,000 g/kg = 4,186.8 J/kg.
- Per degree: 1 °C difference = 1 K difference.
- Result: 1 cal/(g·°C) = 4,186.8 J/(kg·K), which is also 4.1868 kJ/(kg·K) and 1 BTU/(lb·°F).
How to read the result
Liquid water, about 4,182 J/(kg·K) at 20 °C, is unusually high, which is why it stores and carries heat so well. Most metals are far lower: aluminium about 900, iron and steel about 450, copper about 385 J/(kg·K). High specific heat means a material warms and cools slowly; low means it responds quickly. For example, heating 2 kg of water by 30 K takes about 2 × 4,182 × 30 ≈ 251 kJ.
Common mistakes
- Mixing the IT calorie (4.1868 J) with the thermochemical calorie (4.184 J).
- Confusing specific heat (per kg) with heat capacity (for a whole object, in J/K).
- Using a food Calorie (kcal) as if it were a calorie; it is 1,000 times larger.
- Forgetting that specific heat changes with temperature and phase; ice is about half the value of liquid water.
FAQ
Frequently asked questions
Why are cal/(g·°C) and BTU/(lb·°F) equal?
Both were defined from heating water, and the International Table definitions make the ratio exactly 1.
What is the specific heat of water?
About 4.18 kJ/(kg·K) at room temperature, or about 1 cal/(g·°C).
Is J/(kg·°C) the same as J/(kg·K)?
Yes. A change of one degree Celsius equals a change of one kelvin.
Sources: NIST Special Publication 811 (2008), Appendix B, conversion factors · BIPM, The International System of Units (SI Brochure), 9th edition, 2019