Modern Physics for Engineers
Problem Set 10
Problem Set - Due in class, Friday, Dec. 3, 1999.
Problems:
- The sun has a mass of 2e30 kg and a mean radius of
6.4e6 m. If the sun collapsed from a very large, very diffuse cloud of
gas, how much potenital energy would have been converted into thermal energy
during the collapse? Given that the sun is radiating now at the rate of
1340 W/m^2 at the earth (1.5e11 m from the sun), what is the total energy
radiated by the sun per second? How long would the sun "shine" if there were no
other source of energy other than that from gravitational collapse?
- Assuming that the the temperature of the atmosphere of earth
is that same all the way up as it is on the ground and the composition is the
same, find the relationship between pressure and elevation in our atmosphere.
(Your freshman physics text may be helpful for this. Check out Pascal's
principle. Remember, however, that the density of a gas is proportional to
the pressure.) What would you predict the pressure to be outside an airplane
flying at 40,000 ft.?
- Given equation 15.20 in your book, how many photons/m^3 are
there in intergalactic space due to the 2.7 ^oK black body radiation? Compare this with the average number of protons which is about 1 atom/m^3. Compare the
total energy density of the photons to the energy density of the protons.
- The density of protons at 1 atom/m^3 is about 1/12 that needed
to close the universe. The number density of each type of neutrino should be the same as the number density of photons. How massive would one of the neutrinos have to be to "close" the universe?
- SM&M 15-22