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jok3333 [9.3K]
3 years ago
14

A) Show that the surface temperature of a star can be inferred from measurements of blackbodyfluxes at two different frequencies

, even if the stellar radius and distance are unknown.
b) Explain why in practice this method does not work well if both frequencies are on theRayleigh-Jeans side of the spectrum,hνkT.
c) Derive a simple, approximate expression for the temperature when both measurements areon the Wien tail,hνkT.
d) Derive an expression for the star’s radius if a distance measurement is also available (e.g.,from parallax).

Physics
1 answer:
Roman55 [17]3 years ago
3 0

Answer:

The answers to the questions have been solved in the attachment.

Explanation:

The answers to part a to e are all contained in the attachment. For answer part b, temperature and frequency were assumed to be fixed or constant. V² is directly proportional to T telling us that variation in T gives us a square in the frequency variation. This tells us why it is difficult when both frequencies are on this side of the black body.

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Determine the length of the tungsten filament in a 100 watt lightbulb given: (i) the resistivity of tungsten is 5.6 × 10−8 Ω · m
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Answer:

0.34148 m

Explanation:

\rho = Resistivity of tungsten = 5.6\times 10^{-8}\ \Omega m

d = Diameter = 0.0018 inch

r = Radius = \dfrac{r}{2}=\dfrac{0.0018}{2}=0.0009\ in

r=0.0009\times 0.0254=0.00002286\ m

\alpha = Temperature coefficient of tungsten = 0.0045 /^{\circ}C

Power is given by

P=\dfrac{V^2}{R}\\\Rightarrow R=\dfrac{V^2}{P}\\\Rightarrow R=\dfrac{120^2}{100}\\\Rightarrow R=144\ \Omega

We have the equation

R_2=R_1[1+\alpha(T_2-T_1)]\\\Rightarrow R_1=\dfrac{R_2}{1+\alpha(T_2-T_1)}\\\Rightarrow R_1=\dfrac{144}{1+0.0045(2550-25)}\\\Rightarrow R_1=11.64812\ \Omega

Resistance is given by

R=\rho\dfrac{l}{A}\\\Rightarrow l=\dfrac{RA}{\rho}\\\Rightarrow l=\dfrac{11.64812\times \pi (0.00002286)^2}{5.6\times 10^{-8}}\\\Rightarrow l=0.34148\ m

The length of the filament is 0.34148 m

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pogonyaev

Column A: x-axis, input, domain

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Read 2 more answers
HELP
Sergeu [11.5K]

Answer:

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