Homework #18, complete by Friday, Nov 6

1. Email me your draft web page link.

2. You decide to have a cup of coffee with cream. When first poured, the coffee is too hot to drink. Should you add the cream immediately or after several minutes, if you wish to cool the coffee down as quickly as possible? Explain your conclusion, using the equation for heat transfer via conduction.

3. The following solid objects, made of the same material, are maintained at a temperature of 300 K in an environment whose temperature is 350 K: a cube of edge length r, a sphere of radius r, and a hemisphere of radius r. Rank the objects according to the net rate at which thermal radiation is exchanged with the environment, greatest first.

4. In interstellar space, the typical particle density is 1 particle per cm3. Assuming the average temperature of space to be 3K and assuming the particle is H2 (with a diameter of 0.200 nm), determine the mean free path of the particle and the average time between collisions.

5. Chapter 12 Exercise 12.X.3

6. Chapter 12 Review Question 18

7. Chapter 12 Review Question 19

8. In this problem, you will make simple estimates of the temperature of the Earth by assuming that it behaves like a blackbody. In these estimates, you will assume that as a black body in thermal equilibrium, it reradiates as much thermal radiation as it receives from the Sun. Assume also that the surface of the Earth is at a constant temperature over the day-night cycle.
(a) First, calculate the temperature of the surface of the Earth ignoring the atmosphere. To do this, calculate the flux on Earth received from the Sun and the power intercepted by the Earth. Assume that this power goes into heating the Earth and then is reemitted by the Earth as a blackbody. Find the temperature associated with the blackbody emission and compare to the actual temperature of the Earth. Use the following information: T(Sun's surface) = 5800 K, radius of Sun = 7 x 108 m, distance between the Earth and the Sun = 1.5 x 1011 m.
(b) The calculation above would be more correct for a planet without an atmosphere. Atmospheres introduce a complication, because they are transparent to some wavelengths, allowing this radiation to reach the surface, and opaque to other wavelengths, absorbing and then reradiating these wavelengths. The Earth's atmosphere is transparent to visible radiation, but opaque to many other wavelengths, including the infrared. The peak wavelength of radiation emitted by the Earth's surface lies in the infrared (why?). We can estimate the effect of Earth's atmosphere by adopting a simple model atmosphere, consisting of one layer transparent to visible, but opaque to infrared. Assume again that the atmosphere is in thermal equilibrium, reradiating as much power back to space as the incoming solar power. However, the atmosphere is transparent to the incoming solar radiation, so its temperature is maintained by the absorption of infrared radiation radiated from Earth's surface. Assume that half of the atmosphere's radiation is directed out toward space and that the other half is directed towards the surface. Also assume that the power radiated by the surface is equal to the power incoming from the Sun. Using this model, calculate how many times higher the temperature of the Earth is with an atmosphere than without (using your result from a). This is a simple model of the greenhouse effect.

(Problems partly based on Haliday, Resnick, Walker; Kittel; Owen & Morrison.)

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Last updated November 3, 2009