Welcome to Cosmology and Thermodynamics

Thermodynamic Calculations.  

An essential feature of this subject is that matter has properties;  these include pressure, temperature, density, specific heat capacity, enthalpy, internal energy, entropy, ionization energy and many more.  These properties must be taken into account in Cosmology and Astrophysics.

Therefore it is not sufficient for a cosmologist to say

"The Universe is expanding, therefore it must be cooling down", - this statement must be justified by calculations in which the thermodynamic properties of hydrogen are applied.  (The Universe is believed to be mostly hydrogen).  Evaluating and applying these thermodynamic properties is not a simple matter.

Above 1.2 x 104 K hydrogen is all ionized,

below this temperature it starts to associate to atoms,

   i.e.   H+   +  e-   -->  H

therefore the energy of ionization is given up,

which is  1.318 x 109   Joules per kg

Note that this is an enormous figure.

In the range 3500 to 1200 K hydrogen is mostly atomic.

Below 1000 K hydrogen is in the form of molecules,

   i.e.   2H  -->  H2   

the conversion of atoms to molecules involves dissociation energy,

which is  4.36 x 108    Joule per kg-mole.

The temperature ranges quoted are approximate because they are pressure-dependent.

A curve of internal energy of hydrogen versus temperature is displayed in the diagram below.  The reader should note the kinks in the curve;  these are important for understanding the validity, - or otherwise, - of the Hot Big Bang Theory.

It should also be noted that the relationship between temperature and volume is not a smooth curve because there are kinks in the curve in the zones of ionization and dissociation. The same applies to relationships

between temperature and enthalpy and

between temperature and entropy.

These thermodynamic properties are displayed in a Temperature-Entropy Diagram for hydrogen, which has never been available before. The important point to understand is that a Temperature-Entropy Diagram (T-S)  contains a wealth of information which has a number of uses.

(1) It presents numerical thermodynamic data which are necessary for doing calculations;

(2) The scientist or engineer can trace out on the diagram the operation line for a particular action such as an expansion or a compression; invalid actions, e.g. those which violate the Laws of Thermodynamics, can be eliminated.

(3) A T-S Diagram provides an insight into the way that the non-ideal properties of a gas affect thermodynamic operations.

(4) This visual approach to Thermodynamics is easier to understand than dry equations;  in any case many of these equations are not applicable to the areas of dissociation and ionization.

These points are explained with a number of examples in my book.  Some of the results of my calculations are shown in the diagram on the home page of this website.

This Temperature-Entropy Diagram is published in my book and as a separate item; a large scale chart is obtainable from me. It is not feasible to display this diagram on the internet.