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Dimensions and units of a constant

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Wize University Physics Textbook (Master) > Foundations / Introduction / Measurement

Units

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This is the Stefan-Boltzmann equation. σ\sigma is the Stefan-Boltzmann constant.
PA=σT4\frac{P}{A} = \sigma T^4


a) Knowing that P=[ML2T3]P = [\frac{ML^2}{T^3}] is power, A=[L2]A = [L^2] an area, what are the dimensions of the constant?





b) In SI units, it has a value of 5.67×10−185.67 \times 10^{-18} . What would the units be in SI units?





c) Now write the constant in units oflbsK4day3\frac{lbs}{K^4day^3}. (1kg = 2.2lbs)






More Units Questions:
Finding the exponent from dimensional analysis
X=YZ32WnX = \frac{Y Z}{32 W^n}
If X=[Mθ]X = [M\theta] , Y=[MT2]Y = [MT^2] , Z=[θ/L2]Z = [\theta / L^2] , and W=[T/L]W = [T/L] , what is the exponent n?
Dimensions and units of a constant
This is the Stefan-Boltzmann equation. σ\sigma is the Stefan-Boltzmann constant.
PA=σT4\frac{P}{A} = \sigma T^4
a) Knowing that P=[ML2T3]P = [\frac{ML^2}{T^3}] is power, A=[L2]A = [L^2] an area, what are the dimensions of the constant?
Counting heartbeats
How many times does your heart beat in a year?
Fermi question: paperclips
How many paperclips can you fit in an average cup (1 m3=1000 L)?
Filling your tub
How much water (in m3) can you keep in your bathtub without it spilling?
Let's say you are a really fast runner. I mean, like 50km/h fast. Convert that into the following units.
Symbols
In dimensional analysis, the symbol for time is
T
, for mass is
M
, for length is
L
.
In the SI unit system, the symbol for nanogram is
ng
, for millikelvin is
mK
, and centinewton is
cN
.
Power of a variable from dimensions
If the dimensions of the variables
W=[L3] , X =[MT] , Y=[M6L], Z =[M2T]W=[L^3]\ ,\ X\ =\left[\frac{M}{T}\right]\ ,\ Y=\left[\frac{M^6}{L}\right],\ Z\ =\left[M^2T\right]
What is the exponent n?