Understanding Specific Heat Capacity Units: J/(kg·K) and cal/(g·°C)
Specific heat capacity measures the amount of heat energy required to raise the temperature of one unit mass of a substance by one degree of temperature. The two most common units are the SI unit joule per kilogram-Kelvin (J/(kg·K)) and the cgs unit calorie per gram-Celsius (cal/(g·°C)).
One J/(kg·K) is defined as the energy in joules needed to increase the temperature of 1 kilogram of a substance by 1 Kelvin. It is widely used in modern engineering, physics, and thermodynamics due to its consistency with the SI system. Practical applications include:
One cal/(g·°C) originates from the calorie (cal), defined as the heat required to raise 1 gram of water by 1°C. This unit is still common in chemistry, food science, and some legacy engineering fields. Water has a specific heat of exactly 1 cal/(g·°C) or 4.184 J/(g·°C) (or 4184 J/(kg·K)). The conversion factor between the two units is small: 1 J/(kg·K) = 0.0002390057361376673 cal/(g·°C). This is because 1 cal = 4.184 J and 1 kg = 1000 g, so the conversion involves both energy and mass scaling.
Why the Conversion Matters
Accurate conversion is critical when working with international standards or comparing data from different sources. For example, a material's specific heat reported as 800 J/(kg·K) in an SI table would be expressed as approximately 0.1912 cal/(g·°C) in cgs units. Engineers often need to bridge these systems when designing equipment like boilers, radiators, or thermal management systems.
Joule per kilogram-Kelvin to Calorie per gram-Celsius Conversion Reference Table
Joule per kilogram-Kelvin (J/(kg·K))
Calorie per gram-Celsius (cal/(g·°C))
0.1
2.3901e-05
0.5
1.1950e-04
1.0
2.3901e-04
2.0
4.7801e-04
5.0
0.0012
10.0
0.0024
20.0
0.0048
50.0
0.012
100.0
0.0239
500.0
0.1195
1000.0
0.239
Example: Convert 10 J/(kg·K) to cal/(g·°C)
Start with the value: \( 10 \, \text{J/(kg·K)} \)
Multiply by the conversion factor: \( 0.0002390057361376673 \, \text{cal/(g·°C)} / (\text{J/(kg·K)}) \)
Perform the calculation: \[ 10 \times 0.0002390057361376673 = 0.002390057361376673 \]
Thus, a material with a specific heat of 10 J/(kg·K) requires only 0.00239 calories to raise 1 gram by 1°C. This small value highlights the difference in scale between the two units.
Because the calorie is defined as 4.184 joules, and the gram is 1/1000 of a kilogram. Therefore, when converting from J/(kg·K) to cal/(g·°C), you are effectively dividing by 4.184 (energy conversion) and dividing by 1000 (mass conversion), resulting in a factor of 1/(4.184 × 1000) ≈ 0.000239. This means that one J/(kg·K) is a much smaller specific heat increment than one cal/(g·°C).
The conversion factor is universal for any substance because it only depends on the definitions of joule, kilogram, calorie, gram, Kelvin, and Celsius. The specific heat of water is exactly 1 cal/(g·°C) or 4184 J/(kg·K), but the conversion between the two unit systems applies to all materials. Always ensure you use the correct base units: J/(kg·K) and cal/(g·°C) scale linearly with mass and heat energy.
"On fait la science avec des faits, comme on fait une maison avec des pierres ; mais une accumulation de faits n'est pas plus une science qu'un tas de pierres n'est une maison." "Science is built up of facts, as a house is built of stones; but an accumulation of facts is no more a science than a heap of stones is a house." — Henri Poincaré (French Mathematician, Theoretical Physicist & Mining Engineer)