Given the Following Blackbody Curve Graph What Color Will Star a Be Blue Red White Yellow

Textbook: Chapter 5

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Thermal Radiation and Blackbodies

Any object with temperature T > 0 emits EM waves ( radiation ) at all wavelengths. If the object is a perfect absorber, it volition not reflect any light. Call this a blackbody. A perfect absorber re-emits all light incident on it. The emitted lite has a special spectrum called a blackbody spectrum. Spectrum is the intensity of the line every bit the function of wavelength Blackbody spectrum is continous and merely depends on the surface temperature of the object.

The Sun radiation is near blackbody

Plot of Intensity of Blackbody radiation versus wavelength for T = 5,000 Yard:

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Properties of the Blackbody Spectrum

• Shape of the blackbody curve is the same for all temperatures.

• As T increases, the intensity of light at all wavelengths increases.

• The wavelength with the brightest light is denoted   &lambda_max

• Every bit T increase this peak wavelength becomes shorter in inverse proportion to the temperature ( Wien'south Law ):
  

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The Colour of Stars

• Stars take spectra which are very close to a blackbody.
• The colour of a star will depend on its temperature.

The Lord's day's Spectrum The black curve represents the Lord's day's spectrum. The red curve represents the spectrum of a perfect blackbody with surface temperature T=5800 K. The Sun's spectrum can exist approximated past a blackbody spectrum. The peak wavelength for a 5800 M blackbody is at wavelength = 0.0029 / (5.8 x ten3) one thousand = (2.ix/5.8) 10 10-3-3 m = 0.5 x 10-6 k = 500 nm. The summit wavelength is for greenish-yellow calorie-free. But the Sun is putting out similar amounts of blue and ruby-red light. The overall upshot is approximately white light with a yellow tint.

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What Colour Will a Star Appear To Accept?

Example: A star with surface temperature T = 1.ii x ten⁴K

The summit wavelength for this star is at wavelength = 0.0029 / (i.2 ten 104) 1000 = (2.9/1.ii) x x-3-4 m = ii.iv x ten-seven m = 240 nm. The peak wavelength is ultraviolet, which our eyes can't detect. The star emits light in all of the visible range, just emits more than blue low-cal than red lite. Therefore the star volition announced to be a blue-white colour. Our optics aren't very sensitive to violet light, so the tint will appear to be closer to blue than violet.

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Example: A star with surface temperature T = 3x10³K

The acme wavelength for this star is at wavelength = 970 nm. The superlative wavelength is in the infrared role of the spectrum. The star emits light in all of the visible range, merely emits more red calorie-free than blue lite. The star will appear to be reddish.

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The Energy Flux of a Blackbody

• Every bit T increases, the intensity of light at all wavelengths increases.

• The Free energy Flux of an object is the rate that free energy is emitted from a square meter of the object'due south surface.

• F = Free energy Flux

• Units of F are J/(s mⁱⁱ) = West/(m^two).
• 1 Watt = 1 Joule/2d or W=J/s.

• A blackbody has an energy flux which depends only on its Temperature.
• The formula is ( Stefan'southward Law ):
  

• The constant "sigma" is called the Stefan-Boltzmann constant and is given past:
  

• The temperature in this equation is the surface temperature of the object! The object might be much hotter deep inside, but this doesn't matter.

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The Luminosity of a Blackbody

• The luminosity of a star is the power that it emits.

• Power is the charge per unit that energy is emitted by the star.

• Symbol for luminosity is "L".
• Units for luminosity are Watts = W.

• The luminosity is equal to the Free energy Flux times the surface area of the object (if F is constant over the object).
  Fifty = F x A

• A spherical object, such as a star has a surface surface area, A, given by
  A = iv &pi R²
  where R is the star's radius.

• If the star is a blackbody, so its power output or luminosity is
  L = iv &pi R² &sigma T⁴
  
• The luminosity of a star depends both on its temperature and on its size. The larger and hotter it is, the more powerful information technology will be.

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Next Lecture: Atomic Spectra
Read 1st Ed. pages 105 - 118 or 2nd Ed. pages 103 - 114

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Source: https://sites.ualberta.ca/~pogosyan/teaching/ASTRO_122/lect4/lecture4.html

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