1. In 1965, microwave radiation peaking at a wavelength of 0.107 cm was discovered coming from all directions from space. The presence of this radiation had been predicted by Ralph Alpher (until recently at Union College!) and Bob Hermann in 1948, who predicted that the hot Big Bang start of the Universe would leave behind a background remnant radiation. Due to the expansion of the Universe, the radiation has been redshifted to its current wavelength. To what temperature does the current wavelength correspond? This then is the temperature of space!
2. 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.
3. (a) Calculate the temperature of the surface of the Earth on the assumption
that as a black body in thermal equilibrium, it reradiates as much thermal
radiation as it receives from the Sun. Asuume also that the surface of the Earth is at
a constant temperature over the day-night cycle. Comment on the temperature you
find, compared to the actual temperature of 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 January 29, 2005