Stefan Boltzmann Law Radiation

Introduction :

The emission of electromagnetic waves at the expense of the internal energy of the bodies is known as thermal radiation. Theoretical explanation of the nature of black body radiation finally led to the concept of energy quanta which is the first step toward quantum mechanics enabling us to investigate the secrets of atomic structure and other properties of the substances.

Mathematical Equation for Stefan Boltzmann Law Radiation

oseph Stefan analysed the experimental data about the radiation of the bodies at various temperature and concluded that Emissive power of a (black) body is proportional to the forth power of the absolute temperature
Mathematically P  =  `sigma` AT² .,     where A is the surface area, T is temperature of eh surface in Kelvin scale and `sigma`  is the universal constant called Stefan's constant and its value is 5.670 x0 10^-8 W / m² K⁴ . 
Stefan's law involved the temperature in Kelvin scale not in Centigrade scale. The fourth power of temperature indicates how sensitive the power emitted by a body to temperature changes. Initially  Stefan concluded that the  above equation is valid for any body as he did not perform experiments with black bodies. Later Boltzmann on the basis of principles of thermodynamics showed that the equation is valid only for black bodies. Hence the statement leading to the above equation is called Stefan-Boltzmann law.

Definition for Stefan-boltzmann Law Radiation

A body emits radiation that will be proportional to fourth power of absolute temperature and for any body Stefan-Boltzmann law can be given by        
P  =  e_`lambda` `sigma` AT⁴ .........................(1)
where e_`lambda` is emissivity of the body. Its value ranges from 0 to 1.
For a black body   e_`lambda`  =  1 and for a perfect reflector  e_`lambda` =  0.  For example, for polished aluminium   e_`lambda` = 0.05 as it is an excellent reflector , for soot (carbon black) e_`lambda` = 0.95. Human skin has emissivity about 0.97 in infrared region of electromagnetic waves.
If a body with surface area A and temperature T is kept in surroundings with temperature T_s , it simultaneously emits and absorbs thermal radiation till dynamic thermal equilibrium is attained. Then the net rate of heat flow is given by
P_net      =           P_emitted   -   P_absorbed.
From equation (2) ,  P_emitted  =    e_`lambda` `sigma` AT⁴    and P_absorbed =   e_`lambda` `sigma` AT⁴_s .
Hence  P_net         =        e_`lambda` `sigma` AT⁴      -           e_`lambda` `sigma` AT⁴_s                =        e_`lambda` `sigma` A(T⁴ - T⁴_s ).
After the thermal equilibrium is attained, the body and the surroundings are at the same temperature, the body emits the energy at the same rate as that it absorbs. Hence  P_net  =  0.
If  T  >  T_s the body emits more thermal radiation than it absorbs.
If T < T_s the body absorbs more thermal radiation than it emits.

Lithium

Introduction:

Lithium is the first of group I alkali element. Lithium was discovered by Arvfedson. Litium is rare metal, but is widespread. It is prepared by electrolysis of fused lithium chloride. Amblygonite, Lepidolite, Spodemenn is the ores of lithium. Lithium is a soft, lightest metal. Lithium is used in batteries and medicinal fields.

Lithium

• Symbol -Li.
• The atomic number of lithium is 3.
• The atomic mass of lithium is 6.94.
• The electronic configuration of lithium is 1s² 2s¹.
• Lithium is a solid metal which is silvery in its purest form.
• The valence number of electron is 1. Its tend to loss one electron readily to form li⁺ ion.

Properties of lithium:

Physical properties of Lithium:

The following are physical properties of Lithium:

• Lithium is a soft silvery metal. Fresh lithium is silvery but when it is exposed to air it becomes grayish due to oxidation.
• Lithium is lightest of all the metals, the density is very less. The density of lithium is about 0.534 grams per cubic centimeter.
• Lithium hardness is 0.6 on Mohs scale. Mohs scale is used to represent hardness of the material. We can scratch the lithium with our fingernails.
• The structure of lithium is body centric.
• Lithium is a highly reactive metal, readily forms oxides on the metal surface.
• Lithium is a lightest metal and is a good conductor of heat and electricity.
  • Electrical conductivity – 0.108 10⁶ / cm
  • Thermal conductivity- 0.847 W / cmK
• Lithium posses high boiling and melting points.
  • Boiling point of Lithium is 1,335 degree Celsius
  • Melting point of Lithium is 180.54 degree Celsius.
• Lithium has highest specific heat capacity about 3.6 j/gk

Chemical Properties of Lithium:

The following are chemical properties of Lithium:

• Lithium is highly reactive so it is kept under liquid paraffin or oil to prevent oxidation.
• Lithium reacts with oxygen at high temperature to form oxides, at normal temperature it reacts slowly.
• Lithium is the alkali metal that reacts with nitrogen that forms a black nitrure.
• Lithium reacts with halogens produces salts of lithium.
• Lithium reacts readily with water, liberates hydrogen and forms lithium peroxides.
• Lithium produces crimson red color flame during burning.

Velocity of a Reactions

Introduction to Reactions:

The reactions are defined as " the total number reacting special whose concentration actually alters during the course of chemical reactions. In other words, it is the number of concentration terms which determines the dependence of rate of reactions. For a general reactions numerical value of order of reactions are the sum of all the exponents to which the concentrations in the rate equation are raised.

Velocity of a Reactions:

• The velocity or rate of chemical reactions can be defined and measured as "the rate of formation of  one or more of its products or as the rate of consumption of one or more of its reactants".
• If the reactions are homogeneous and occurs entirely in the gaseous phase, the partial pressure of its components could be measured, and if the reactions takes place in solution.
• Thus, the units of velocity of a reactions in solution will be units of concentration per unit time.
• The velocity of a reactions, depends on the concentration or pressure of the reactants.
• As the concentration of the reactants keep on decreasing from moment to moment so, velocity of a reactions decreases with time.
• In order to decide  the velocity of  reactions at any time.

Expressing velocity of reaction:

• The velocity of reactions are measured in terms of either the rate of decrease in concentration of reaction(s) or the rate of increase in concentration of product(s). Thus, for the reactions A`->` B.

• The velocity of reaction is given by:

`(-d[A])/(dt)` =`(+d[B])/(dt)`

• It must be clearly understood that the velocity of reaction is invariably a positive quantity.
• The minus sign given to -d[A]/dt simply indicates that the concentration of the reactant, A is falling.
• While positive sign given to +d[B]/dt implies that the concentration of the product, B is increasing with the time.

Simultaneous Reactions:

• Some of the simultaneous reactions are:

Parallel reactions:

• The reactions giving the main product is called main reactions, while the other is called parallel or side reactions.
• By altering the conditions of the experiment, the relative rates of the side reactions can be varied and sometimes to such an extent that a side reaction is changed into main or principal reactions and vice-versa.

Consecutive reactions:

• This reactions in which the first reaction product is subsequently converted into a second product.

Consider the process,

Reversible reactions:

• In which the rate of the back reaction in significant.

• Reaction products react among themselves to form the original reactants at significant speed.

Electromagnetic waves transverse or longitudinal

Introduction:

Before going to learn whether the electromagnetic wave is transverse or longitudinal .Let us have a brief review on wave and its characteristics

Wave motion:
 It is a process of transferring energy in a medium in the form of disturbance due to repeated periodic motion of the particle in the mean about their mean position in which the energy is handed over from one particle to other particle by leaving their mean positions.

Mechanical Wave:
A mechanical wave is a periodic disturbance which can be produced only in a material medium and its transfer of energy from one point to other without there being a direct contact between  the two points.

Two types of mechanical waves:

Mechanical waves are classified into

1) Transverse waves

2) Longitudinal waves 

Electromagentic Waves are Transverse

Electromagnetic waves characteristics are similar to transverse waves.
If the particles at a medium vibrate at right angles to the direction of the propagation of the energy then that wave is called as transverse wave. Such waves are produced on the surface of water, in musical instruments. If the stretched strings, the energy the energy travels outwards and the particle of the medium vibrates up and down.

Electromagnetic waves are transverse waves.
The following terms are used in the study of transverse wave or electromagnetic wave:

Amplitude:
It is the maximum displacement of particles from the mean position. The displacement may be in either direction of the mean position.

Period: The period of a wave is the time taken by a wave to complete one oscillation

Frequency: Number of vibrations made by a particle of the medium in one second

Crest and trough of a transverse wave: A crest is a point of a transverse wave which at any instant have the maximum positive  or upward displacement.

Trough: This is defined as the maximum negative or downward displacement.

Wavelength:
For a electromagnetic wave the distance between consecutive crest and trough is called as wave length.
Wave velocity is the energy at which wave is propogated.

Electromagentic Waves are Longitudinal Waves

Longitudinal waves:
Electromagnetic waves can travel through vacuum. Example of the electromagnetic waves is the light waves. This is because light waves are not mechanical waves. A light wave is a periodical disturbance which can travel through vacuum.

These waves are discovered Maxwell and consists of vibrating electric  and magnetic fields since such fields can produce in vacuum and can be propagated in vacuum. the light waves, gamma waves, radio waves and X-rays are some of the examples of electromagnetic waves.

Electromagnetic Wave Intensity

Introduction :

The electromagnetic wave intensity is nothing but the measure of the intensity of the electromagnetic wave in free space or in any medium. It generally depends on the velocity of the electromagnetic wave. It is proportional to the square of the amplitude of the electric or magnetic field.

Before giving a proper definition of electromagnetic wave intensity we first try to understand what electromagnetic waves are. The electromagnetic waves are nothing but the waves produced due to an accelerating or oscillating charge. This wave contains both electric and magnetic field vectors which are perpendicular to each other as well as perpendicular to the direction of the wave propagation.

Define Electromagnetic Wave Intensity:

The electromagnetic wave intensity is defined as the energy crossing per second per unit area perpendicular to the direction of propagation of electromagnetic wave or the average power per unit area transported by an electromagnetic wave.

Example of Electromagnetic Wave Intensity:

For proper understanding of the electromagnetic wave intensity, we consider an example in which the electromagnetic waves are propagated along X-axis with the speed of light. Consider an imaginary cylinder along the X-axis with area of cross section A and length c Δt and the electromagnetic waves are incident normally to the area A and crosses the cylinder as shown in Fig.1. Let u_av be the average energy density of the electromagnetic wave.

         Fig.1 Imaginary cylinder
The energy of electromagnetic wave (U) crossing the area of cross section at P normally in time Δt is the energy of wave contained in a cylinder of length c Δt and area of cross section A. It is given by
                                                            U =u_av (c Δt) A
The intensity of electromagnetic wave at P is
                                                            I = U / A Δt
                                                              = u_av c Δt A / A Δt
                                                              = u_av c
In terms of maximum electric field
                                                            u_av = ε₀ E₀² / 2
so,                                                        I = ε₀ E₀² c / 2 = ε₀ E²_rms c
In terms of maximum magnetic field
                                                            u_av = B₀² / 2μ₀
so,                                                        I = B₀² c / 2μ₀ = B²_rms c / μ₀