Question

CONFIGURE UP RESEARCH PROFILE ON ALL THE BEST POSSIBLE PARADOXES IN ASTROPHYSICS AND QUANTUM MECHANICS

Answer 1

6.Heat death paradox (Clausius paradox)

Assuming that universe is eternal a question arises: How is it that thermodynamic
equilibrium has not been long achieved?
Heat death paradox, otherwise known as Clausius paradox and Thermodynamic paradox, is
founded on the basic assumption that every system tends to achieve thermodynamic equilibrium.
This paradox is based upon the classical model of the universe in which the universe is eternal.
Clausius’ paradox is paradox of paradigm. It was necessary to amend the fundamental ideas
about the universe, which brought about the change of the paradigm. The paradox was solved
when the paradigm was changed. The paradox which is valid in the classical stationary model of
the universe is not so in Fridman’s nonstationary relativistic model. This is a solved paradox and
therefore is an exparadox.
The paradox was based upon the rigid mechanical point of view of the Second principle of
thermodynamics postulated by Rudolf Clausius according to which heat can only be transferred
from a warmer to a colder object. If the universe was eternal, as claimed in the classical
stationary model of the universe, it should already be cold.
This paradox originates from a real phenomenon accessible to human senses and is not a thought
experiment but a real sensory observation. There is no experiment that could demonstrate this
paradox. The paradox is of theoretical nature.

According to recent cosmological theories the universe is not eternal and it began some 15 billion
years ago. In view of this, the solution of the Heat death paradox is that thermodynamic
equilibrium has not been achieved because not enough time has passed.

7.Gibbs’ paradox (paradox of mixing)

Assume that there is a vessel, divided by a barrier into two equal compartments
containing the same gas, in equal quantities, at equal temperature and pressure. The
removal of the barrier and mixing of gas from each compartment causes increase in
system entropy.
This paradox is based in the mixing of gases, providing that practically nothing has changed (gas
quantity, temperature, pressure, volume). When the barrier is removed each of the two quantities
of gas spreads over the entire volume of the vessel changing the system entropy, which is easy to
calculate. Under equal conditions the entropy of separate compartments is equal. Prior to the
removal of the barrier the system entropy is 2S, after the barrier has been removed it is higher
than 2S. This phenomenon is called entropy of mixing. Paradox of mixing comprises of
calculating the entropy of two thermodynamic systems, before and after their contents are mixed.
The paradox was formulated by Willard Josiah Gibbs in 1875. Gibbs first developed the paradox
of mixing in 1861. The paradox of mixing is the former name of Gibbs’ paradox. The paradox is
a “precognitive” introduction into Bose and Fermi statistics.
This paradox originates from a real phenomenon accessible to human senses and is not a thought
experiment. It is a practicable laboratory experiment for paradox interpretation, although its
essence lies in its explanation.
The paradox was formulated and solved by Gibbs himself. He pointed out the possibility of
“misunderstanding“and at the same time explained why it might occur. Thus, this is an
exparadox.
Considering that Gibbs’ paradox exists when the phenomenon is viewed from the standpoint of
classical statistic mechanics, and that the paradox does not exist if it is explained by quantum
statistic, this paradox can be classified as a paradox of paradigm. Changing the basic
paradigmatic principles brings about the solution of the paradox.

It is the fundamental assumption in classical statistic mechanic that identical particles are
distinguishable from one another. System states, resulting from permutation of identical particles,
are indistinguishable from one another. From the point of view of classical statistic entropy has
no additive characteristics. Gibbs concluded that classical statistic mechanics should be treated
as a border case, and that the fundamental assumption should be that identical particles cannot be
told apart. In that case the paradox of mixing does not exist since no work is done by the
movement of particles in the act of invisible mixing.