Understanding Calories per Second-Centimetre-Degree Celsius to Milliwatts per Metre-Kelvin Conversion
The calorie per second-centimetre-degree Celsius, cal/(s-cm-°C), is a large CGS unit of thermal conductivity found in older physics and geology literature. The milliwatt per metre-kelvin, mW/(m-K), is a fine-grained SI unit convenient for low-conductivity materials such as gases, foams, and thermal insulation where the plain W/(m-K) figures would be small decimals. Converting to mW/(m-K) keeps such values readable while staying in SI.
Conversion Formula
To convert Calories per Second-Centimetre-Degree Celsius to Milliwatts per Metre-Kelvin, multiply by this factor:
Step-by-Step Example
Convert 25 Calories per Second-Centimetre-Degree Celsius to Milliwatts per Metre-Kelvin.
How to Convert Calories per Second-Centimetre-Degree Celsius to Milliwatts per Metre-Kelvin
These steps take a CGS conductivity into fine-grained SI units.
- Start with the value: Note the conductivity in cal/(s-cm-°C), such as 25.
- Multiply by 418400: This is the number of mW/(m-K) in one cal/(s-cm-°C).
- Do the arithmetic: .
- Report the result: 25 cal/(s-cm-°C) equals 10,460,000 mW/(m-K).
Calories per Second-Centimetre-Degree Celsius to Milliwatts per Metre-Kelvin conversion table
| Calories per Second-Centimetre-Degree Celsius (cal/(s-cm-°C)) | Milliwatts per Metre-Kelvin (mW/(m-K)) |
|---|---|
| 0 | 0 |
| 1 | 418400 |
| 2 | 836800 |
| 3 | 1255200 |
| 4 | 1673600 |
| 5 | 2092000 |
| 6 | 2510400 |
| 7 | 2928800 |
| 8 | 3347200 |
| 9 | 3765600 |
| 10 | 4184000 |
| 15 | 6276000 |
| 20 | 8368000 |
| 25 | 10460000 |
| 30 | 12552000 |
| 40 | 16736000 |
| 50 | 20920000 |
| 60 | 25104000 |
| 70 | 29288000 |
| 80 | 33472000 |
| 90 | 37656000 |
| 100 | 41840000 |
| 150 | 62760000 |
| 200 | 83680000 |
| 250 | 104600000 |
| 300 | 125520000 |
| 400 | 167360000 |
| 500 | 209200000 |
| 600 | 251040000 |
| 700 | 292880000 |
| 800 | 334720000 |
| 900 | 376560000 |
| 1000 | 418400000 |
| 2000 | 836800000 |
| 3000 | 1255200000 |
| 4000 | 1673600000 |
| 5000 | 2092000000 |
| 10000 | 4184000000 |
| 25000 | 10460000000 |
| 50000 | 20920000000 |
| 100000 | 41840000000 |
| 250000 | 104600000000 |
| 500000 | 209200000000 |
| 1000000 | 418400000000 |
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).
What is the Milliwatt per Metre-Kelvin?
The milliwatt per metre-kelvin is a unit of thermal conductivity equal to one thousandth of a watt per metre-kelvin. Its convenient scale makes it the preferred unit for describing thermal insulators and gases, whose conductivities are small fractions of a watt per metre-kelvin.
Definition
One milliwatt per metre-kelvin is 10⁻³ watt per metre-kelvin, the SI unit of thermal conductivity:
Like its parent unit, it may equivalently be written mW/(m·°C), since a one-kelvin interval equals a one-degree-Celsius interval.
Origin and History
The unit is simply the SI watt per metre-kelvin scaled by the standard milli- prefix (10⁻³). It became common in the insulation, cryogenics and gas-property literature during the twentieth century, where reporting figures such as 26 mW/(m·K) for air is clearer than 0.026 W/(m·K).
Law and Notable Facts
The milliwatt per metre-kelvin is a coherent SI unit with a decimal prefix and is legal for use worldwide. Building-insulation performance is often stated in mW/(m·K): the lower the value, the better the insulator, which is why manufacturers compete to push products below 30 mW/(m·K).
Real-World Examples and Conversions
- Dry air at room temperature conducts heat at about 26 mW/(m·K).
- Mineral wool and glass-fibre insulation typically fall between 30 and 40 mW/(m·K).
- Polyurethane foam boards reach roughly 22–25 mW/(m·K).
- 1 mW/(m·K) = 0.001 W/(m·K); conversely 1 W/(m·K) = 1000 mW/(m·K).
Frequently Asked Questions
How many milliwatts per metre-kelvin equal one cal/(s-cm-°C)?
Exactly 418400 mW/(m-K). This follows because 1 cal/(s-cm-°C) is 418.4 W/(m-K), and each watt is 1000 milliwatts.
How do I convert mW/(m-K) back to cal/(s-cm-°C)?
Multiply by 0.000002390057 (that is, 2.390057 × 10⁻⁶). For example, 418400 mW/(m-K) returns to 1 cal/(s-cm-°C).
Why use milliwatts instead of watts per metre-kelvin?
Insulating materials, gases, and foams have conductivities well below 1 W/(m-K); expressing them in mW/(m-K) avoids long strings of leading zeros and makes small differences easier to read.
What does 25 cal/(s-cm-°C) look like in mW/(m-K)?
It equals 10,460,000 mW/(m-K), a huge figure that reflects a highly conductive metal rather than an insulator.
Is the factor 418.4 related to the calorie definition?
Yes. The thermochemical calorie is defined as exactly 4.184 joules, so 1 cal/(s-cm-°C) scales to 418.4 W/(m-K), and therefore 418400 mW/(m-K).
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Complete Calories per Second-Centimetre-Degree Celsius conversion table
| Unit | Result |
|---|---|
| Watts per Metre-Kelvin (W/(m-K)) | 418.4 W/(m-K) |
| Milliwatts per Metre-Kelvin (mW/(m-K)) | 418400 mW/(m-K) |
| BTU per Hour-Foot-Degree Fahrenheit (BTU/(h-ft-°F)) | 241.7471 BTU/(h-ft-°F) |
| BTU-Inch per Hour-Square Foot-Degree Fahrenheit (BTU-in/(h-ft2-°F)) | 2900.965 BTU-in/(h-ft2-°F) |