Scientific Notation: Multiplying Very Large & Very Small Numbers

Stefan-Boltzmann Law:

E = ϭ T4

 

 

ϭ is the Stefan-Boltzmann constant and is equal to:

5.67 x 10-8 Wm2

 

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Question: If the surface temperature of a star is 3500oK, how much energy does it radiate?

 

Use Stefan-Boltzmann Law:

 

E = ϭ T4

 

E = (5.67 x 10-8 Wm2 ) * (3500oK)4

 

E = (5.67 x 10-8 Wm2 ) * (3500 * 3500 * 3500* 3500)

 

E = (5.67 x 10-8 Wm2 ) * 150,062,500,000,000

 

E = (5.67 x 10-8 Wm2 ) * 1.50625 x 1015

 

 Multiply 5.67 * 1.50625 = 8.5404375

Add the exponents ( -8 + 15) = 7

 

Answer: E= 8.5404375 x 107 Wm2