Answered: (8) By what factor does the total…

(8) By what factor does the total emitted intensity go up if you increase the temperature of a blackbody from 1000 K to 1750 K?

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter28: Quantum Physics

Section: Chapter Questions

Problem 6P

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Check Your Understanding Suppose that two stars, and . radiate exactly the same total power. If the radius of star is three times that of star , what is the ratio of the surface temperatures of these stars? Which one is hotter?
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Even when shut down after a period of normal use, a large commercial nuclear reactor transfers thermal energy at the rate of 150 MW by the radioactive decay of fission products. This heat transfer causes a rapid increase in temperature if the cooling system fails (1 watt = 1 joule/second or 1 W = 1 J/s and 1 MW = 1 megawatt). (a) Calculate the rate of temperature increase in degrees Celsius per second (C/s) if the mass of the is 1.60105 kg and it has an average specific heat of 0.3349 kJ/kg . C. (b) How long would it take to obtain a temperature increase of 2000 C, which could cause some metals holding the radioactive materials to melt? (The initial rate of temperature increase would be greater than that calculated here because the heat transfer is concentrated in a smaller mass. Later, however, the temperature increase would slow down because the 500,000-kg steel containment vessel would also begin to heat up.)
Unreasonable results. (a) Find the sped of hydrogen sulfide, H2S, molecules at a temperature of 250 K. Its molar mass is 31.4 g/mol (b) The result isn't very unreasonable, but why is it less reliable than those for, say, neon or nitrogen?
(a) Repeat Exercise 31.2, and convert the energy to joules or calories. (b) If all of this energy is converted to thermal energy in the gas, what is its temperature increase, assuming 50.0 cm3 of ideal gas at 0.250atm pressure? (The small answer is consistent with the fact that the energy is large on a quantum mechanical scale but small on a macroscopic scale.)
What is the critical magnetic field for lead at T = 2.8 K?
How much does the power radiated by a blackbody increase when its temperature (in K) is tripled?
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As the very first rudiment of climatology, estimate the temperature of Earth. Assume it is a perfect sphere and its temperature is uniform. Ignore the greenhouse effect. Thermal radiation from the Sun has an intensity (the "solar constant" S) of about 1370 W/m2 at the radius of Earth's orbit. (a) Assuming the Sun's rays are parallel, what area must S be multiplied by to get the total radiation intercepted by Earth? It will be easiest to answer in tens of Earth's radius, R. (b) Assume that Earth reflects about 30% of the solar energy it intercepts. In other words, Earth has an albedo with a value of A=0.3 . In terms of S, and R, what is the rate at which Earth absorbs energy from the Sun? (c) Find the temperature at which Earth radiates energy at the same rate. Assume that at the infrared wavelengths where it radiates, the emissivity e is 1. Does your result show that the greenhouse effect is important? (d) How does your answer depend on the area of Earth?
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