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Simplify units

Saf Al

Posted 10 years ago

Hi, I was trying to solve a simple equation using variables with units as follows: UnitConvert[ Module[{n = 1.46, \[Lambda] = Quantity[ 630 10^-9, "Meters"], Tf = Quantity[1400, "Kalvin"], \[Beta]T = UnitConvert[Quantity[6.8 10^-12, "Centimeters" ^2/"Dynes"], "Meters" ^2/(("Kilograms" "Meters")/("Seconds")^2)], Kb = UnitConvert[Quantity[1, "Poltzmann constant"]]}, \[Alpha]Scat = (8 \[Pi]^3)/( 3 \[Lambda]^4) (n^2 - 1) Kb Tf \[Beta]T], ( "Kilometers")^-1] // UnitSimplify When the previous code is executed, it seems that UnitSimplify can't cancel the Kalvin dimension in the resulting unit. It would be helpful if somebody can explain this. Regards

Hi,

I was trying to solve a simple equation using variables with units as follows:

UnitConvert[
  Module[{n = 1.46, \[Lambda] = Quantity[ 630 10^-9, "Meters"], 
    Tf = Quantity[1400, "Kalvin"], \[Beta]T = 
     UnitConvert[Quantity[6.8 10^-12, "Centimeters" ^2/"Dynes"], 
      "Meters" ^2/(("Kilograms" "Meters")/("Seconds")^2)], 
    Kb = UnitConvert[Quantity[1, "Poltzmann constant"]]},
   \[Alpha]Scat = (8 \[Pi]^3)/(
     3 \[Lambda]^4) (n^2 - 1) Kb Tf \[Beta]T], (
  "Kilometers")^-1] // UnitSimplify

When the previous code is executed, it seems that UnitSimplify can't cancel the Kalvin dimension in the resulting unit. It would be helpful if somebody can explain this.

Regards

POSTED BY: Saf Al

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Saf Al

Posted 10 years ago

I see. Thanks for the clarification.

POSTED BY: Saf Al

Anderson Coser Gaudio

Anderson Coser Gaudio, Federal University of Espirito Santo

Posted 10 years ago

You are right. Mathematica has some tolerance when dealing with units and constants. Unfortunately it was not true in the case of Kalvin. Mathematica interpreted "Kalvin" as "Kelvins difference" (DeltaK) and, as a consequence, it was unable to cancel the the Ks. Look at the codes below. t1 = Quantity[1400, "Kelvin"] t2 = Quantity[1400, "Kalvin"] t1 == t2 1400 K 1400 K Quantity::compat: Kelvins and KelvinsDifference are incompatible units >> Quantity::compat: Kelvins and KelvinsDifference are incompatible units >> 1400 K == 1400 K and t1 = Quantity[1400, "KelvinsDifference"] t2 = Quantity[1400, "Kalvin"] t1 == t2 1400 K 1400 K True Regards.

You are right. Mathematica has some tolerance when dealing with units and constants. Unfortunately it was not true in the case of Kalvin. Mathematica interpreted "Kalvin" as "Kelvins difference" (DeltaK) and, as a consequence, it was unable to cancel the the Ks. Look at the codes below.

t1 = Quantity[1400, "Kelvin"]
t2 = Quantity[1400, "Kalvin"]
t1 == t2


1400 K
1400 K
Quantity::compat: Kelvins and KelvinsDifference are incompatible units >>
Quantity::compat: Kelvins and KelvinsDifference are incompatible units >>
1400 K == 1400 K

and

t1 = Quantity[1400, "KelvinsDifference"]
t2 = Quantity[1400, "Kalvin"]
t1 == t2

1400 K
1400 K
True

Regards.

POSTED BY: Anderson Coser Gaudio

Saf Al

Posted 10 years ago

My bad. However. It seems that Mathematica is kind of broad minded, when it comes to "Poltzmann" instead of "Boltzmann", That's to say, it shows the same constant with the same dimensions. Thanks for the answer.

POSTED BY: Saf Al

Anderson Coser Gaudio

Anderson Coser Gaudio, Federal University of Espirito Santo

Posted 10 years ago

Try to use "Kelvin" instead of "Kalvin". If you use "Boltzmann" in the place of "Poltzmann", this will help you even more.

POSTED BY: Anderson Coser Gaudio

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