Understanding Watts per Metre-Kelvin to Calories per Second-Centimetre-Degree Celsius Conversion
The watt per metre-kelvin (W/(m·K)) is the SI unit of thermal conductivity. The calorie per second-centimetre-degree Celsius (cal/(s·cm·°C)) is a CGS-based unit still seen in older physics literature, materials-science tables and thermal-property databases. Because the calorie and centimetre are both smaller-scale units, one W/(m·K) corresponds to only a small fraction of a cal/(s·cm·°C).
Conversion Formula
To convert Watts per Metre-Kelvin to Calories per Second-Centimetre-Degree Celsius, multiply by this factor:
Step-by-Step Example
Convert 25 Watts per Metre-Kelvin to Calories per Second-Centimetre-Degree Celsius.
How to Convert Watts per Metre-Kelvin to Calories per Second-Centimetre-Degree Celsius
Map an SI conductivity value onto the CGS calorie-based unit found in legacy tables.
- Record the SI value: take the conductivity in W/(m·K).
- Multiply by 0.002390057: this converts directly to cal/(s·cm·°C).
- Note the calorie basis: remember the exact anchor is 418.4 W/(m·K) per cal/(s·cm·°C).
- Worked result: 25 W/(m·K) × 0.002390057 = 0.05975143 cal/(s·cm·°C).
Watts per Metre-Kelvin to Calories per Second-Centimetre-Degree Celsius conversion table
| Watts per Metre-Kelvin (W/(m-K)) | Calories per Second-Centimetre-Degree Celsius (cal/(s-cm-°C)) |
|---|---|
| 0 | 0 |
| 1 | 0.002390057 |
| 2 | 0.004780115 |
| 3 | 0.007170172 |
| 4 | 0.009560229 |
| 5 | 0.01195029 |
| 6 | 0.01434034 |
| 7 | 0.0167304 |
| 8 | 0.01912046 |
| 9 | 0.02151052 |
| 10 | 0.02390057 |
| 15 | 0.03585086 |
| 20 | 0.04780115 |
| 25 | 0.05975143 |
| 30 | 0.07170172 |
| 40 | 0.09560229 |
| 50 | 0.1195029 |
| 60 | 0.1434034 |
| 70 | 0.167304 |
| 80 | 0.1912046 |
| 90 | 0.2151052 |
| 100 | 0.2390057 |
| 150 | 0.3585086 |
| 200 | 0.4780115 |
| 250 | 0.5975143 |
| 300 | 0.7170172 |
| 400 | 0.9560229 |
| 500 | 1.195029 |
| 600 | 1.434034 |
| 700 | 1.67304 |
| 800 | 1.912046 |
| 900 | 2.151052 |
| 1000 | 2.390057 |
| 2000 | 4.780115 |
| 3000 | 7.170172 |
| 4000 | 9.560229 |
| 5000 | 11.95029 |
| 10000 | 23.90057 |
| 25000 | 59.75143 |
| 50000 | 119.5029 |
| 100000 | 239.0057 |
| 250000 | 597.5143 |
| 500000 | 1195.029 |
| 1000000 | 2390.057 |
What is the Watt per Metre-Kelvin?
The watt per metre-kelvin is the SI coherent unit of thermal conductivity, quantifying how readily a material conducts heat. It expresses the rate of heat flow through a material per unit thickness for each degree of temperature difference across it.
Definition
A material has a thermal conductivity of one watt per metre-kelvin if a temperature gradient of one kelvin per metre drives a heat flux of one watt per square metre through it:
Because a temperature difference of one kelvin equals one degree Celsius, W/(m·K) and W/(m·°C) are numerically identical.
Origin and History
The unit follows directly from Fourier's law of heat conduction, published by Joseph Fourier in his 1822 Théorie analytique de la chaleur, which states that heat flux is proportional to the negative temperature gradient. The proportionality constant is the thermal conductivity, and it acquired its coherent SI form once the watt, metre and kelvin were established within the International System of Units.
Law and Notable Facts
The watt per metre-kelvin is the standard SI unit for material property tables worldwide. Thermal conductivity spans an enormous range: from aerogels near 0.02 W/(m·K), among the best solid insulators, to diamond at roughly 2000 W/(m·K), the highest of any bulk natural material.
Real-World Examples and Conversions
- Still air conducts heat at about 0.026 W/(m·K); water at about 0.6 W/(m·K).
- Common window glass is near 1.0 W/(m·K); stainless steel about 15 W/(m·K).
- Copper reaches roughly 400 W/(m·K), which is why it is used for heat sinks.
- 1 W/(m·K) = 1000 mW/(m·K) ≈ 0.5778 BTU/(h·ft·°F).
What is the Calorie per Second-Centimetre-Degree Celsius?
The calorie per second-centimetre-degree Celsius is the CGS-based unit of thermal conductivity, historically common in physics and physical-chemistry literature. It measures the heat in calories flowing per second through a one-centimetre thickness for each degree Celsius of temperature difference.
Definition
One calorie per second-centimetre-degree Celsius represents a heat flow of one calorie per second through a one-centimetre cube per degree Celsius across it. Using the thermochemical calorie (4.184 J):
The value follows from 4.184 J/s per (0.01 m · 1 K) = 4.184 ÷ 0.01 = 418.4 W/(m·K). If the International Table calorie (4.1868 J) is used instead, the factor is 418.68 W/(m·K).
Origin and History
The unit arose in the CGS era, when heat was measured in calories, lengths in centimetres and temperature in degrees Celsius. It appears throughout older thermal-conductivity tables and heat-transfer texts, especially in chemistry and metallurgy, before the watt per metre-kelvin became standard.
Law and Notable Facts
Though largely superseded by SI, the unit is still encountered in legacy data and some scientific traditions. Its large size is convenient for metals: because 1 cal/(s·cm·°C) equals 418.4 W/(m·K), even highly conductive copper is under 1 in these units, whereas most materials are small fractions.
Real-World Examples and Conversions
- Copper conducts at about 0.94 cal/(s·cm·°C), i.e. roughly 400 W/(m·K).
- Iron is about 0.18 cal/(s·cm·°C).
- Water is roughly 0.0014 cal/(s·cm·°C).
- 1 cal/(s·cm·°C) = 418.4 W/(m·K); conversely 1 W/(m·K) ≈ 0.00239 cal/(s·cm·°C).
Frequently Asked Questions
How many cal/(s·cm·°C) equal 1 W/(m·K)?
One watt per metre-kelvin equals about 0.002390057 cal/(s·cm·°C). The small number reflects that the calorie-centimetre unit is comparatively large.
Which calorie is used in this unit?
This uses the thermochemical/steam calorie basis where 1 cal/(s·cm·°C) equals exactly 418.4 W/(m·K), the standard adopted in most conductivity tables.
How do I reverse the conversion?
Multiply the cal/(s·cm·°C) value by 418.4 to get W/(m·K); that is the reverse factor for this pair.
Where might I encounter cal/(s·cm·°C)?
It appears in older CGS-era physics and materials-science references, geophysics literature, and legacy thermal-property databases.
What is 100 W/(m·K) in cal/(s·cm·°C)?
Multiply 100 by 0.002390057 to get about 0.2390057 cal/(s·cm·°C).
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Complete Watts per Metre-Kelvin conversion table
| Unit | Result |
|---|---|
| Milliwatts per Metre-Kelvin (mW/(m-K)) | 1000 mW/(m-K) |
| BTU per Hour-Foot-Degree Fahrenheit (BTU/(h-ft-°F)) | 0.5777893 BTU/(h-ft-°F) |
| BTU-Inch per Hour-Square Foot-Degree Fahrenheit (BTU-in/(h-ft2-°F)) | 6.933472 BTU-in/(h-ft2-°F) |
| Calories per Second-Centimetre-Degree Celsius (cal/(s-cm-°C)) | 0.002390057 cal/(s-cm-°C) |