6 Extras

6.8.1

Problem 6.8.1

What is more important for the open space suit: heating or cooling function?

solution

In spite of wide-spread opinion that the pace is very cool place (the temperature is lower than $3\,K$), the cold as a cooling rate can be considered in different aspects. The heat conductivity in vacuum is also close to zero, therefore the heat flow from a warm body placed into open space can go only due to the radiation. The radiation intensity is proportional to fourth degree of the temperature. For example, if an astronaut gets into the open space (and far from near stars, so that heating from extra sources can be neglected) and cannot return to the spacecraft, he (or she) will not be covered by icy crust and there is no danger of fast icy death. His (or her) temperature (about $310 \, K$) is sufficient to stay in comfortable temperature conditions some time, at least to arrival of space rescue team. Under assumption that there is no heat production in astronaut's body and precipitation of water from the skin is also absent (the astronaut is inside the hermetic space suit without the heat insulation), then it will coll down in one degree approximately every forty minutes, even in absolutely black space suit, which emits energy the most efficiently. Along with decreasing of temperature the cooling rate will also decrease in accordance with the Stephan-Boltzmann law. Actually an astronaut in vacuum is in danger of overheat rather than cold, because the heat production rate in human body equals approximately $100 \,W$; efficient heat removal represent one of the most challenging problems faced by the space suit developers.

6.8.2

Problem 6.8.2

If the Universe is electrically neutral then how many electrons are there for each baryon?

solution

$8/9.$

6.8.3

Problem 6.8.3

Explain why the thermonuclear processes in the first stars considerably influenced the evolution of the Universe as a whole?

solution

A nuclear fusion reaction yields approximately $7\cdot 10^6\, eV$ of energy per hydrogen atom, while the hydrogen atom ionization energy is just $13.6\,\mbox{\it eV}.$ Therefore it is sufficient to convert quite small fraction ($\sim 10^{- 5}$) of total baryon mass of stars in order to ionize the rest of Universe. In fact one needs a fraction at lest one order of magnitude greater. The reason is that 1) only part of photons have energy above the ionization threshold; 2) due to the redshift each hydrogen atom suffers multiple recombinations.

6.8.4

Problem 6.8.4

Why is the present relative abundance of chemical elements approximately the same as right after the creation of the Solar system?

solution

Energy required for nuclear transformations must be of order of nuclei bound energy. Putting aside the lightest nuclei, a rough estimate for the bound energy per nucleon is of order of $8\, MeV.$ Therefore the energy needed for nuclear transformations is million times grater than the one obtained in chemical reactions. Such energies (or temperatures) cannot be achieved in any natural process on Earth. Thus the presently observed relative abundance of elements is approximately the same that was $4.6\cdot 10^9$ years ago when the Solar System was formed. The radioactive elements make exclusion. Changes of their abundance present one of the methods to determine the age of Universe.