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Chapter 6: Q41E (page 1315)

Two stars, both of which behave like ideal blackbodies, radiate the same total energy per second. The cooler one has a surface temperature Tand a diameter 3.0times that of the hotter star. (a) What is the temperature of the hotter star in terms of T? (b) What is the ratio of the peak-intensity wavelength of the hot star to the peak-intensity wavelength of the cool star?

Short Answer

Expert verified
  1. The temperature of the hotter star is 1.732 T.
  2. The ratio of the peak-intensity wavelength of the hot star to the peak-intensity wavelength of the cool star is 0.577

Step by step solution

01

Determine the temperature of the hotter star

a. Use the definition of intensity of radiation

We know that both the stars have the same power P, and the diameter of the cooler star istimes the hotter one, thus,

So,

Therefore, the temperature of the hotter star is 1.732 T.

02

Determine the ratio of the wavelengths of both the stars

b. Use Wien displacement law to find the peak wavelength of each star

Divide both the equations

Therefore, the ratio of the peak-intensity wavelength of the hot star to the peak-intensity wavelength of the cool star is 0.577

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