Modern Physics

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PHY251 Homework Set 5 Reading: Chapter 4 and 5 Homework: Chapter 4, Questions 2,4 Problems 4,5,6,7 Chapter 5, Problems 2,22 Hints and Solutions Question IV.2 If you peer through a small hole in a very hot oven, you see a glow that clearly suggests the presence of light waves. This is the blackbody radiation in the oven. If you peer through a hole in a freezer, will there be blackbody radiation inside? What if anything, distinguishes this radiation from the radiation you see in the oven? Hints: No hints Solution: The radiation from the freezer exists just like the radiation from a hot oven, and in fact for any object with temperature T > 0 K. In the case of the freezer, when you open its door, the total radiation from the environment (kitchen sink, your body in front of it, etc.) is more ( E ~ σ T 4 ) than the blackbody radiation from the freezer. The freezer's radiation is also at much longer wavelength ( λ peak · T = 2.9×10 -3 m·K; peak = 2.9×10 -3 m·K / 263 K = 11.0 μm) below the infrared region. Question IV.4 If Earth were only half its actual distance from the Sun, would the average temperature of Earth change? If so, by about what factor? State the assumptions you must make to be able to give a rough estimate of the factor. Hints: No hints Solution: The surface of the Earth presented to the Sun, would be four times larger in the case the distance were reduced by a factor two, so the energy received , E rec , would be four times what it is today. The Earth radiates the energy back to space, proportional to T 4 , so that an equilibrium is established: E rec = ασ T 4 , with T the current average temperature, and α some proportionality factor that
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solutions 05 - phy251_hw05 PHY251 Homework Set 5 Reading...

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