Problem 2: Black hole – the ultimate blackbodyA black hole emits blackbody radiation called Hawking radiation. A black hole with massM has a total energy of Mc², a surface area of 167G²M² /c*, and a temperature ofhc³/167²KGM.a) Estimate the typical wavelength of the Hawking radiation emitted by a 1 solarmass black hole (2 × 103ºkg). Compare your answer to the size of the black hole.b) Calculate the total power radiated by a one-solar mass black hole.c) Imagine a black hole in empty space, where it emits radiation but absorbs nothing.As it loses energy, its mass must decrease; one could say "evaporates". Derive adifferential equation for the mass as a function of time, and solve to obtain anexpression for the lifetime of a black hole in terms of its mass.

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Answered: Problem 2: Black hole – the ultimate…

University Physics Volume 3

17th Edition

ISBN:9781938168185

Author:William Moebs, Jeff Sanny

Publisher:William Moebs, Jeff Sanny

Chapter6: Photons And Matter Waves

Section: Chapter Questions

Problem 57P: (a) For what temperature is the peak of blackbody radiation spectrum at 400 nm? (b) If the...

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A perfect black body has its surface temperature 27 cº Determine : Maximum radiation wavelength? Black body radiation intensity? The rate of energy released from 2m² Tungsten wire had its radiating surface area 8mm² and its temperature 2100K, considering that the wire is an ideal black body, Calculate the energy that the wire radiates in 10 minutes. Suppose the surface temperature of the Sun were about 12,000K, rather than 6000K. a. How much more thermal radiation would the Sun emit? b. What would happen to the Sun's wavelength of peak emission? c. Do you think it would still be possible to have life on Earth? Explain /A The energy radiated by a black body at 2300K is found to have the maximum at a wavelength 1260 nm, its emissive power being 8000W/m2. When the body is cooled to a temperature T K, the emissive power is found to decrease to 500W/m2. Find : (i) the temperature T k (ii) the wave length at which intensity of emission in maximum at the Te / Black body becomes yellow with λ…
For the purpose of this exercise, we consider the Earth as a blackbody at a temperature of 300K. a. Assuming that it is spherical with a radius equals to 6370 km, calculate the total amount energy emitted by the Earth (Hint: The total amount of energy emitted by a surface = amount of energy emitted per unit area x area of the surface). b. What wavelength range would you recommend to measure radiation emitted by the Earth using a satellite mounted sensor?
QUESTION1: Stefan-Boltzman law can be used to estimate H emitted from a surface where H = AeoT, where H = surface area (m2) in units of watts, e = diffusivity characterizing the spreading properties of the surface, o = a universal constant called the Stefan-Boltzman constant. (-5.67x108 W m?K4) and T = absolute temperature (K). a) Determine the error of the radiation H of a steel sphere surface with radius = 0.15 + 0.02 m, e 0.90+ 0.05 and T = 550 ± 25 K. Compare your results with the exact error. Calculations b) radius = 0.15 0.01 m, e 0.90 +0.025 Repeat for T = 550 12.5 K. and Interpret your results.
Question A7 The intensity of the emitted radiation by a star is at a maximum at a wavelength of 78.9 nm. a) Calculate the surface temperature of the star. b) Calculate the ratio of the intensity radiated at 65.0 nm to the maximum intensity. Assume that the star radiates like an ideal blackbody.
docs.google.com a Q.4 A- Define a blackbody, discuses experimental data for the distribution of energy in blackbody radiation at three temperatures. B- A surveyor uses a steel measuring tape that is exactly 15.000 m long at a temperature of 30°C. The markings on the tape are calibrated for this temperature. (a) What is the length of the tape when the temperature is 35°C? (b) When it is 45°C, the surveyor uses the tape to measure a distance. The value that she reads off the tape is 40.794 m. What is the actual distance?
The blackbody radiation emitted from a furnace peaks at a wavelength of 3.5 x 10-6 m (0.0000035 m). What is the temperature inside the furnace? K.
Answer the following A. A comet has just passed the Earth and its peak emission is observed at 15000 nm. Determine in which region of the electromagnetic spectrum (e.g. X-ray, infrared, visible, ultraviolet, ...) the peak emission wavelength resides. What is the temperature of the comet? B. Within the Solar System, a convenient unit of measurement is the Earth-Sun distance, called an astronomical unit (AU). For bigger distances, we use the light year (LY), the distance that light travels in one year. We can expand our lingo to include other measures of distance, for example, light days, light minutes, and light hours. Starting with the values you can look up in the Appendices for the speed of light and the astronomical unit, calculate how many “light minutes” there are in 1 AU. C. What is the observable universe? How big is it?
The Sun radiates almost like a perfect blackbody at a temperature of T= 5800 K. a) Show, using the Stefan-Boltzmann law, that the rate at which it radiates energy is - 4x1026 W. b) If you were at Earth's orbit, in space, how many Sun photons would reach you per second? Assume you have a mass of 70 kg, are spherical and full of water. You may need to find your cross sectional area and assume all Sun photons move in the same direction.
How would you calculate what is the percentage of the blackbody radiation from a source at 300 K in the wavelength region from 8 to 14 um? (This is the so-called window in the earth's atmosphere.) Do not solve it numerically just explain how you would solve it (write the necessary equation).
A furnace emits radiation at 2000 K. Treating it as black body radiation, calculate the wavelength at which the emission is maximum. a.) 1.449 x 10 ^ -6 m b.) 2.449 x 10 ^ -6 m c.) 3.449 x 10 ^ -6 m d.) 4.449 x10 ^ -6 m
Problem-1: An asteroid is hurtling toward earth at 150,000“. The temperature of the asteroid is about 100 K, meaning that its peak emission is 2 = 29 µm. The speed of light is c = 3E[8]. a) What is the wavelength of light that we receive from the asteroid? (Answer: 2.89855E[-05] m)
Problem 3. Compute the maximum possible effective surface temperature for a star like the Sun, i.e., M = Mo, R, = Ro. What does your result tell you about the internal structure of the Sun?

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