b_a - 1.1) One may use any reasonable equation to obtain...

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Unformatted text preview: 1.1) One may use any reasonable equation to obtain the dimension of the questioned quantities. I) The Planck relation is 1 2 1 ] ][ [ ] [ ] [ ] ][ [-- = = ⇒ = ⇒ = T ML E h E h E h ν ν ν (0.2) II) 1 ] [- = LT c (0.2) III) 2 3 1 2 2 2 ] ][ ][ [ ] [--- = = ⇒ = T L M m r F G r m m G F (0.2) IV) 1 2 2 1 ] [ ] [ ] [--- = = ⇒ = K T ML E K K E B B θ θ (0.2) 1.2) Using the Stefan-Boltzmann's law, 4 θ σ = Area Power , or any equivalent relation, one obtains: (0.3) . ] [ ] [ ] [ 4 3 1 2 4---- = ⇒ = K MT T L E K σ σ (0.2) 1.3) The Stefan-Boltzmann's constant, up to a numerical coefficient, equals , δ γ β α σ B k G c h = where δ γ β α , , , can be determined by dimensional analysis. Indeed, , ] [ ] [ ] [ ] [ ] [ δ γ β α σ B k G c h = where e.g. . ] [ 4 3-- = K MT σ ( )( )( )( ) , 2 2 2 3 2 1 2 2 2 3 1 1 1 2 4 3 δ δ γ β α δ γ β α δ γ α δ γ β α----- + + + +--------- = = K T L M K T ML T L M LT T ML K MT (0.2) The above equality is satisfied if, - =-- =---- = + + + = +- ⇒ , 4 , 3 2 2 , 2 3 2 , 1 δ δ γ β α δ γ β α δ γ α (Each one (0.1)) ⇒ = =- =- = . 4 , , 2 , 3 δ γ β α (Each one (0.1)) ⇒ ....
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This note was uploaded on 11/08/2011 for the course PHYS 0000 taught by Professor Na during the Spring '11 term at Rensselaer Polytechnic Institute.

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b_a - 1.1) One may use any reasonable equation to obtain...

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