Why statistical mechanics was introduced?

When we consider bodies at macroscopic level they consist of uncountable atoms or molecules i.e about 10^23 atoms/gm mole. In such cases we cannot predict the result of interactions between atoms with the help of ordinary classical laws of motion. In order to solve such a situation, a new branch of science called statistical mechanics is introduced.

Statistical mechanics is the branch of science which establishes the interpretation of macroscopic behavior of system in terms of its microscopic properties. It doesn't deal with motion of each particle but it takes into account the average or most probable properties of system with out going into interior details of characteristics of its constituents.

The larger the number of particles in the physical system considered, the more nearly correct are statistical predictions.

Before the advent of quantum theory, Maxwell, Boltzmann, Gibbs etc applied statistical methods making the use of classical physics. These statistical methods are known as "classical statistics" or "maxwell boltzmann statistics".

These statistics explained successfully many observed physical phenomenon like temperature, pressure, energy etc; but couldn't explain adequately several other experimentally observed phenomenon like black body radiation, specific heat at low temperature etc.

In order to explain such phenomenon "quantum statistics" was introduced and developed by Fermi, Dirac, Bose, Einstein with new approach by using new quantum idea of discrete exchange of energy between system.

    

What is the reaction cross section for Helium-3 and boron-10 isotopes for thermal neutrons?

The reaction crossection for Helium-3 is 5330 Barns and that for Boron-10 is 3840 Barns.
Both the reactions are strongly  dependent on incident neutron energy 'E' and have roughly a 1/sqrt(E) dependence.

Small trick for designers using capacitors

Suppose you require a smaller capacitance with higher voltage rating for your application but you are left with only higher capacitance capacitor with less voltage rating. How could you overcome this problem?

You can follow a small trick. You put two or more capacitors in series to arrive at your designed capacitance of smaller value.Because
i) It divides the voltage over two capacitors and thus has net effect of doubling (in case of two capacitors) the voltage rating.
ii) It reduces overall capacitance by following

C = (C1*C2) / (C1+C2 )

where 'C' is total capacitance of two capacitors in series.

For instance, consider two capacitors 100 pF @500VDC,

Then keeping them in series we get C = 50pF

voltage is now divided over two capacitors so total rating is 50pF @1000V Dc.

Hope this is helpful for designers.

What is Decibel?

The human ear has logarithmic characteristics i.e. the loudness of sound is proportional to log of power which causes it.

Suppose a certain sound power 'P' produces a loudness 'L'. Now let loudness be increased to 'mL' by increasing power to 'kP'.(k, m are constants)

If loudness is again increased by same amount i.e 2mL, it is found that power required is K^2 * P.

If process is repeated 'N' times then

Pn = K^N * P  ---> log(Pn / P) =N*logK

N = [log(Pn/P)] / log K

taking natural log of above equation we get

N = K*log(Pn/P)

but napiers logs are difficult to work.

taking logs to base 10 we arrive at

N = 10 * log10(Pn/P) 

where 'Pn' is power derived and 'P' is power absorbed. 

The unit of above equation is decibel.

Checking capacitors with an ohmmeter

Set the range of Ohm meter to higher range greater than 1MOhm. The ohm-meter leads are to be connected across leads of capacitor. Fora good capacitor, the meter first shows low value and then slowly recedes to a higher value. The reading gets stabilized to  a higher value after some time due to charging action.

For ceramic, paper and Mica capacitors, the resistance falls in the range 500 - 1000 MOhm.
For electrolytic capacitors, it is around 1MOhm.

If ohmmeter reading immediately goes to zero and stays there, the capacitor is short circuited.

If capacitor shows no charging action but just reads very high resistance it may be open.

Stray capacitance:

The wiring and components in a circuit have capacitance to metal chassis. The stray capacitance is typically 5 to 10PF.  

Leakage resistance of capacitor: 

Consider a capacitor charged by a DC voltage source. If the source is removed a perfect capacitor would keep its charge indefinitely.