The Earth reradiates the energy it receives from the Sun as a black body.  We can calculate the effective temperature of the Earth using the Stefan-Boltzmann equation F = sT4  where we solve for the Temperature T.  We use for the energy flux the amount of energy absorbed per second Le divided by the Earth's surface area from which the energy is radiated 4pd2 so that the flux is = Le/(4pd2).  Here d is the radius of the Earth given above and s is the Stefan-Boltzmann constant.  And the effective temperature is:Te4 = (Le/(4pd2))/s   =    Le/(4spd2)  = __________________ K4and taking the square root of Te4 twice in succession we get the effective Temperature Te:Te  = [Le/(4spd2)]0.25  =  _________________ Kfor the temperature of the effective Earth.  What is the temperature in the Celsius scale?  __________ C.  (Do I need to tell you how to convert from Kelvin to Celsius?  If you don't know look it up in your textbook!!)

Consider an electron gyrating in the magnetic field associated with a sunspot which has a magnetic field strength of 0.25 T. The typical temperature of a sunspot is 3500 K the equipartition equation for velocity v, temperature T and mass m of a particle, is, 3kgT V = m kB is Boltzmann's constant (1.38×10–23 J/K). a) The mass of the Sun is approximately 2 × 1030 kg. Use this information and the infor- mation given above to compute the acceleration g due to gravity at the surface of the Sun. b) Compute the drift velocity Ūg due to gravity for a proton and an electron located within a sunspot. c) Assuming a typical mass density of the Sun's photosphere of 10-3 kg/m³, compute the number density of protons and electrons in the photosphere (where sunspots reside) assuming that the Sun is comprised of pure ionized hydrogen. d) Calculate the total current density J (accounting for the contributions of both electrons and tons) within sunspots. You may assume that you can treat the ensemble of…

Multiple-Concept Example 6 explores the approach taken in problems such as this one. Quasars are believed to be the nuclei of galaxies in the early stages of their formation. Suppose a quasar radiates electromagnetic energy at the rate of 1.5 × 104¹ W. At what rate (in kg/s) is the quasar losing mass as a result of this radiation? Number i A quasar at the center of a spiral galaxy Units

In kinetic theory of gases, atoms are modeled as point masses m with mean speed v related to temperature T by m v^2 = 3 k T, where k is Boltzmann’s constant. Assuming gas atoms travel several thousand Angstroms between collisions with each other, how cool would hydrogen gas need to be before quantum mechanics would have to be taken into consideration?

Two stars, both of which behave like ideal blackbodies, radiate the same total energy per second. The cooler one has a surface temperature T and 4.0 times the diameter of the hotter star. What is the temperature of the hotter star in terms of T? (Just write the result)

If the human body is well approximated by a black body with tem- perature T = 310◦ K (98.6◦ F). At what wavelength (λ) do we emit the most energy (λmax)? How much energy per area (flux) do we emit? Remember the value of the Stefan-Boltzmann constant is σ = 5.67 × 10−5erg/(cm2K4s1). What kind of radiation (region of the electromagnetic spectrum) do we emit most of?