About Temperature Units

The relationship between different temperature units involves an offset in addition to the usual scale factor. The offset is often not important to the physics equations because these equations are concerned only with temperature differences. There are, however, some cases where an absolute or thermodynamic temperature measure must be used. One example is the Stefan-Boltzmann law for blackbody radiation used in radiation boundary conditions.

The SI unit system uses the kelvin, which is an absolute temperature, as the basic unit of temperature. English unit systems use degree Fahrenheit as the basic unit of temperature, which, because the Fahrenheit scale is not absolute, is fine for most purposes except radiation. For such purposes, the Rankine scale provides the corresponding absolute temperature unit. See Table 3-27 for a list of acceptable unit syntax.

Table 3-27: Temperature Units
Scale	Unit
Celsius	[degC]
Fahrenheit	[degF]
Kelvin	[K]
Rankine	[R] or [Ra]

Differential vs. Absolute Temperature

If the dimension of an expression that includes a unit is temperature or 1/temperature, COMSOL interprets the dimension as an absolute temperature. If the dimension is something other than temperature but the unit expression includes temperature, the temperature is a differential temperature; that is, COMSOL uses no offset when converting between different temperature units.

The following examples show how the unit conversion works for different expressions that include temperature units:

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100[degC] is an expression that has temperature as the dimension. COMSOL interprets it as an absolute temperature and evaluates it as 373.15 K.

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373.15[1/K] is interpreted as an absolute inverse temperature (but no conversion is necessary from kelvin to kelvin).

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373.15[1/degC] evaluates to 100[1/K] using the offset of 273.15 degrees between kelvin and degrees Celsius.

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100[degC/K] is dimensionless, and the temperature is therefore a differential temperature; that is, the result is 100 because the conversion uses no offset.

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To make the COMSOL Multiphysics software interpret 100[degC/K] as an absolute temperature, split the expression using two separate expressions such as 100[degC][1/K], which equals 373.15. This is also what occurs when you use a variable (TC, for example) defined as 100[degC]. TC[1/K] is then also two expressions where both are interpreted as absolute temperature.

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For temperature units that require an offset and a scale factor to be converted to kelvin, it is not possible to convert them simply using a multiplication. While 293.15[K][1/degF] produces the expected output, 68 (68 degrees Fahrenheit corresponds to 293.15 kelvin), 293.15[K]*1[1/degF] evaluates to something completely different. As mentioned in the previous point, 293.15[K/degF] uses no offset and is also usually not the desired expression.