Dimension
SpeedofLightc
GravitationalConstantG
ReducedPlanckConstantℏ
ElectricConstant
ϵ
0
BoltzmannConstant
1ΩW/
2
k
Time
-1
-2
-1
4
-2
-6
Mass
0
-1
1
-1
1
2
Length
1
3
2
-3
2
4
ElectricCurrent
0
0
0
2
0
-2
AbsoluteThermodynamicTemperature
0
0
0
0
-1
-2
In[]:=
FirstNullSpace
-1
-2
-1
4
-2
-6
0
-1
1
-1
1
2
1
3
2
-3
2
4
0
0
0
2
0
-2
0
0
0
0
-1
-2

Out[]=
{1,0,1,1,-2,1}
In[]:=
InnerPower,
c
,
G
,
ℏ
,
ε
0
,
k
,Most@%29,Times
Out[]=
1
ε
0
ℏ
c
/
2
k
In[]:=
UnitDimensions[%32]​​UnitDimensions
1
ΩW/
2
K

Out[]=
{{ElectricCurrentUnit,2},{LengthUnit,-4},{MassUnit,-2},{TemperatureUnit,2},{TimeUnit,6}}
Out[]=
{{ElectricCurrentUnit,-2},{LengthUnit,4},{MassUnit,2},{TemperatureUnit,-2},{TimeUnit,-6}}
In[]:=
Entity["PhysicalQuantity","WiedemannFranzLawRatio"]["Dataset"]
Out[]=
abbreviations
—
algebraic types
{positive real,scalar}
alternate names
—
base physical quantity
—
canonical unit
1ΩW/
2
K
classes
{}
dimensions
{{ElectricCurrentUnit,-2},{LengthUnit,4},{MassUnit,2},{TemperatureUnit,-2},{TimeUnit,-6}}
entity classes
{}
instances
—
name
Wiedemann-Franz law ratio
named SI unit
—
physical property type
—
quantity variable
WiedemannFranzLawRatio
SI base unit
1
2
kg
4
m
/(
6
s
2
A
2
K
)
SI unit
1ΩW/
2
K
standard identifiers

standard symbols

symbols
{}
In[]:=
JoinAssociation#->0&/@UnitDimensions
1
ΩW/
2
K
[[All,1]],AssociationRule@@@UnitDimensions
1
ΩW/
2
K

Out[]=
ElectricCurrentUnit-2,LengthUnit4,MassUnit2,TemperatureUnit-2,TimeUnit-6
​
In[]:=
Values[%]
Out[]=
{-2,4,2,-2,-6}
In[]:=
<|
c
->JoinAssociation#->0&/@UnitDimensions
1
ΩW/
2
K
[[All,1]],AssociationRule@@@UnitDimensions
c
,
1
ΩW/
2
K
->JoinAssociation#->0&/@UnitDimensions
1
ΩW/
2
K
[[All,1]],AssociationRule@@@UnitDimensions
1
ΩW/
2
K
|>
Out[]=

c
ElectricCurrentUnit0,LengthUnit1,MassUnit0,TemperatureUnit0,TimeUnit-1,
1
ΩW/
2
K
ElectricCurrentUnit-2,LengthUnit4,MassUnit2,TemperatureUnit-2,TimeUnit-6
In[]:=
Values/@Values[%]
Out[]=
{{4,-6,-2,2,-2},{-2,4,2,-2,-6}}
In[]:=
JoinAssociationMapJoinAssociation#->0&/@UnitDimensions
1
ΩW/
2
K
[[All,1]],Association[Rule@@@UnitDimensions[#]]&,
c
,
G
,
ℏ
,
ε
0
,
k
,<|
1
ΩW/
2
K
->JoinAssociation#->0&/@UnitDimensions
1
ΩW/
2
K
[[All,1]],AssociationRule@@@UnitDimensions
1
ΩW/
2
K
|>
Out[]=

c
ElectricCurrentUnit0,LengthUnit1,MassUnit0,TemperatureUnit0,TimeUnit-1,
G
ElectricCurrentUnit0,LengthUnit3,MassUnit-1,TemperatureUnit0,TimeUnit-2,
ℏ
ElectricCurrentUnit0,LengthUnit2,MassUnit1,TemperatureUnit0,TimeUnit-1,
ε
0
ElectricCurrentUnit2,LengthUnit-3,MassUnit-1,TemperatureUnit0,TimeUnit4,
k
ElectricCurrentUnit0,LengthUnit2,MassUnit1,TemperatureUnit-1,TimeUnit-2,
1
ΩW/
2
K
ElectricCurrentUnit-2,LengthUnit4,MassUnit2,TemperatureUnit-2,TimeUnit-6
In[]:=
MatrixForm[NullSpace@Transpose[Values/@Values[%70]]]
Out[]//MatrixForm=
(
1
0
1
1
-2
1
)
In[]:=
PhysicalConstantDimensionalCombinations[physicalquantity_?QuantityQ,physicalconstants_List]:=Inner[Power,physicalconstants,Most@First[NullSpace[Transpose[Values/@Values[Join[AssociationMap[Join[Association[#->0&/@UnitDimensions[physicalquantity][[All,1]]],Association[Rule@@@UnitDimensions[#]]]&,physicalconstants],<|physicalquantity->Join[Association[#->0&/@UnitDimensions[physicalquantity][[All,1]]],Association[Rule@@@UnitDimensions[physicalquantity]]]|>]]]]],Times]
In[]:=
PhysicalConstantDimensionalCombinations
1
ΩW/
2
K
,
c
,
G
,
ℏ
,
ε
0
,
k

Out[]=
1
ε
0
ℏ
c
/
2
k
In[]:=
UnitConvert
1
ΩW/
2
K
,1
1
ε
0
ℏ
c
/
2
k

Out[]=
1.468517169×
9
10
2
k
/(
ε
0
ℏ
c
)
In[]:=
PhysicalConstantSystemConvert[physicalquantity_?QuantityQ,physicalconstants_List]:=UnitConvert[physicalquantity,1/Inner[Power,physicalconstants,Most@First[NullSpace[Transpose[Values/@Values[Join[AssociationMap[Join[Association[#->0&/@UnitDimensions[physicalquantity][[All,1]]],Association[Rule@@@UnitDimensions[#]]]&,physicalconstants],<|physicalquantity->Join[Association[#->0&/@UnitDimensions[physicalquantity][[All,1]]],Association[Rule@@@UnitDimensions[physicalquantity]]]|>]]]]],Times]]
In[]:=
PhysicalConstantSystemConvert
1
ΩW/
2
K
,
c
,
G
,
ℏ
,
ε
0
,
k

Out[]=
1.468517169×
9
10
2
k
/(
ε
0
ℏ
c
)
​