Questions Using Wien’s Law and Stefan’s Law

1 A star has a λmax  of 650nm and a radius of 700 000 km..

(i)	Use Wein’s Law to calculate its surface temperature.
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(ii)	Calculate its surface area
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(iii)	Use Stefan’s law to calculate its power output.

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2	Use Stefan’s Law to calculate the surface area of the Sun assuming that its power output is 3.6 x1026W andd its surface temperature is 5 700K

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2.	Assume the Sun to have a radius of  14.9 x 1011m ( this is actually the  distance of the Earth to the Sun).
(i)	Calculate the volume of this sphere.

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(ii)	Knowing the real power output of the Sun, what would the power output of the Sun be per square metre if it were to have the radius given in question (i)?
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(iii)	What is the power that we expect to arrive at Earth per square metre of surface at the equator?
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3.	(a)	State the meaning of T in the Stefan-Boltzmann law.
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	State the unit of luminosity.
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 (b)	The graph shows how λmax (the wavelength of the peak of the radiation spectrum) for a range of stars varies with the surface temperatures of the stars.

	Carry out appropriate calculations to show that this graph is consistent with Wien’s law.
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(3)

	Use the graph to estimate the surface temperature of a star whose intensity peaks at a wavelength of 0.4 µm.
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(1)
	This star has a radius of 9.0 × 107 m. Calculate its luminosity.
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 (b)	The graph shows the energy distribution in the spectra of two stars bCar and bAnd.

	What can be deduced about the colours of the two stars from the graph?
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(1)
	Estimate the surface temperature of bAnd.
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	The luminosity of βCar is 2.0 × 1028 W and it has a surface temperature of 9300 K. Calculate the surface area of βCar.
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(3)
	By comparing the areas under the two graphs, estimate the luminosity of βAnd.
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(2)
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