What is criticality in a Nuclear reactor?

Let us assume that a reactor is producing 1 Watt of power steadily as a result of 3.1 x 10^10 fissions per second.

The number of Neutrons available for fission at any time remains same during criticality condition. When the chain reaction is maintained steady, the power level is steady and the reactor is said to be critical.

If the power is increasing or decreasing, the rate of neutron production is not constant.

The neutron multiplication factor, K, based on the neutron cycle is used to keep track of neutron production.

K = number of neutrons in a generation / number of neutrons in preceding generation

For instance, consider 100 neutrons, which is our first generation.

If K=1, there will be 100 neutrons at beginning of second generation, 100 at third generation and so on. Fissions continue at the same rate as at the beginning.

If K>1, say 1.05, the 100 neutrons of first generation produce 100 x 1.05 = 105 neutrons at the beginning of next generation.

After 100 generations, the number of neutrons present would be 13150 i.e.100 x (1.05)^100.

The power would be increasing and is said to be super critical. In this case the power increased 131 times in about one tenth of a second. This is too fast to control and in practice multiplication factor is never allowed to become so large.

If K<1, the neutron population decreases with time and power decreases and reactor is said to be subcritical.

 

   

Third Law of Thermodynamics ( The Law of zero entropy )

"Nernst" in 1906 proposed a general priniciple supported by series of experimental tests on problem of atomic heat at low temperatures. it was proposed as " The new heat theorem " and is called as third law of thermodyanmics.

Nernst statement

                       " The heat capacities of all solids tend to zero as the absolute zero of temperature is approached and   that the internal energies and entropies of all substances become equal there, approaching their common value asymptotically".

This law neither follows from first law or second law nor is totally a new law.

Other statement of Nernst:

                        " No entropy change takes place when pure crystalline solid reacts at absolute zero".

 Plank statement:

                        " The entropy of a solid or a liquid is zero at absolute zero of temperature".

Lewis and Randall statement 

                       "Every system has finite positive entropy, but at the absolute zero of temperature the entropy may become zero and does so become in the case of a pure crystalline substance".      

But this statement is confined to pure crystalline solids because theoretical argument and experimental evidence have shown that the entropy of solutions and super cooled liquids is not zero even at absolute zero.

For instance, ice always has residual entropy at absolute zero. It also doesn't apply to amorphous class of substances like glass etc.

Importance of third law of thermodynamics

• Third law is useful in explaining the nature of bodies in neighborhood of absolute zero.
• It permits the calculations of absolute values of entropy and physical interpretation of thermodynamic properties such as Helmholtz & Gibbs free energies etc.
• It can be conceived that as the temperature of system tends to absolute zero, its entropy tends to a constant value which is of pressure and state of aggregation etc. 

 "Nernst" formulated that "the entropy change in isothermal reversible process of condensed system approaches zero as temperature at which the process occurs approaches zero".

The principle of Barthelot states that "every chemical transformation which takes place with out the intervention of external energy tends towards the production of that substance or systems of substance which will give the greatest development of heat i.e that process is realized which is most exothermic.