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I'm trying to use Mathematica units more often, but I've run into the following problem:

    (*Define some unitful constants*)
    q = UnitConvert[Quantity["elementary charge"]];
    k = UnitConvert[Quantity["Boltzmann Constant"]];
    T = Quantity[300, "Kelvin"];
    V = Quantity[5, "Volt"];
    (*Do a simple calculation*)
    UnitConvert[(q V)/(k T)]

The above code outputs

    Quantity[193.409, ("Kelvins")/("KelvinsDifference")]

which really should just be 193.409, since the units cancel, but Mathematica insists on a distinction between absolute temperature and temperature differences. I understand that such a distinction is useful in conversions, but the above is quite a nuisance.

Is there a way to prevent this? I'd rather not have to put in QuantityMagnitude calls every time I need to cancel some Kelvins.


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I think this behaviour has changed: Kelvin used to be interpreted by Wolfram Alpha as KelvinDifference, whereas Kelvins was recognized by Mathematica as a built-in unit and directly interpreted as Kelvin. Since a few months, Kelvin is interpreted as Kelvins, so the error appears to have gone away. (Of course, the unit of the Boltzmann constant is stilll incorrect, see Xerxes' answer.) –  Martin J.H. Nov 10 '14 at 11:30

1 Answer 1

up vote 16 down vote accepted

This appears to be a bug. The dimensions of the Boltzmann constant are incorrect. In fact, all the physical constants I checked have TemperatureUnit where they should have TemperatureDifferenceUnit. You should only have to make a substitution when making calls to physical constants in Quantity:

q = UnitConvert[Quantity["elementary charge"]];
k = (UnitConvert[Quantity["Boltzmann Constant"]] /. 
   "Kelvins" -> "KelvinsDifference");
T = Quantity[300, "Kelvin"];
V = Quantity[5, "Volt"];
UnitConvert[(q V)/(k T)]
(* 193.409 *)

EDIT: Alternatively, since Quantity seems to be calling away to Alpha, you could do

k = UnitConvert[Quantity["Boltzmann Constant (energy per temperature difference)"]]
share|improve this answer
Thanks! I agree: it makes a lot more sense for those to be TemperatureDifferenceUnit. And your fix solves my problem! –  Sam Bader Mar 7 '13 at 1:29

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