0. If two systems are in thermal equilibrium with a third system, then they must be in thermal equilibrium with each other. 1. http://scienceworld.wolfram.com/physics/timg81.gif, where dE is the energy change, http://scienceworld.wolfram.com/physics/timg83.gif is the change in heat, dW is the work done, T is the temperature (http://scienceworld.wolfram.com/physics/Temperature.html), dS is the change in entropy (http://scienceworld.wolfram.com/physics/Entropy.html), P is the pressure (http://scienceworld.wolfram.com/physics/Pressure.html), and dV is the volume change. 2. The second law of thermodynamics prohibits the construction of a perpetual motion machine (http://scienceworld.wolfram.com/physics/PerpetualMotionMachine.html) of `the second kind.' A consequence is the result that http://scienceworld.wolfram.com/physics/timg87.gif. 3. As temperature (http://scienceworld.wolfram.com/physics/Temperature.html) goes to 0, the entropy (http://scienceworld.wolfram.com/physics/Entropy.html) S approaches a constant http://scienceworld.wolfram.com/physics/timg88.gif. Combining the first and second laws gives the combined law of thermodynamics (http://scienceworld.wolfram.com/physics/CombinedLawofThermodynamics.html)
http://scienceworld.wolfram.com/physics/timg89.gif

The first law of thermodynamics is a consequence of conservation of energy (http://scienceworld.wolfram.com/physics/ConservationofEnergy.html) and requires that a system may exchange energy with the surroundings strictly by heat (http://scienceworld.wolfram.com/physics/Heat.html) flow or work (http://scienceworld.wolfram.com/physics/Work.html). Therefore, for change in energy dE, heat (http://scienceworld.wolfram.com/physics/Heat.html) change http://scienceworld.wolfram.com/physics/fimg129.gif, work (http://scienceworld.wolfram.com/physics/Work.html) done dW, http://scienceworld.wolfram.com/physics/fimg131.gif


For a reversible process (http://scienceworld.wolfram.com/physics/ReversibleProcess.html) in which only expansive work is considered, the first law takes the form http://scienceworld.wolfram.com/physics/fimg132.gif


where T is the temperature (http://scienceworld.wolfram.com/physics/Temperature.html), dS the entropy (http://scienceworld.wolfram.com/physics/Entropy.html) change, P the pressure (http://scienceworld.wolfram.com/physics/Pressure.html), and dV volume change.

Conservation of Energy


If the forces acting on a particle are conservative so that there exists a function http://scienceworld.wolfram.com/physics/cimg270.gif such that http://scienceworld.wolfram.com/physics/cimg271.gif


then the total energy http://scienceworld.wolfram.com/physics/cimg272.gif

given as the sum of kinetic energy (http://scienceworld.wolfram.com/physics/KineticEnergy.html) and potential energy (http://scienceworld.wolfram.com/physics/PotentialEnergy.html) is a constant

Energyhttp://scienceworld.wolfram.com/images/tealtab_topright.gif
http://scienceworld.wolfram.com/images/gradient-teal.gifhttp://scienceworld.wolfram.com/images/spacer.gifhttp://scienceworld.wolfram.com/images/spacer.gif
Energy is an abstract quantity of extreme usefulness in physics because it is defined in such a way that the total energy of any closed physical system is always constant (conservation of energy (http://scienceworld.wolfram.com/physics/ConservationofEnergy.html)). It is impossible to overstate the importance of this concept in all branches of physics from elementary mechanics to general relativity (http://scienceworld.wolfram.com/physics/GeneralRelativity.html). Energy is measured in units of mass times velocity squared, and the MKS (http://scienceworld.wolfram.com/physics/MKS.html) and cgs (http://scienceworld.wolfram.com/physics/cgs.html) units of energy are the Joule (http://scienceworld.wolfram.com/physics/Joule.html) and erg (http://scienceworld.wolfram.com/physics/Erg.html), respectively. Other common units of energy include the Btu (http://scienceworld.wolfram.com/physics/Btu.html), calorie (http://scienceworld.wolfram.com/physics/Calorie.html), and kilowatt hour (http://scienceworld.wolfram.com/physics/KilowattHour.html).

The important quantity in physics known as work (http://scienceworld.wolfram.com/physics/Work.html), which is the product of applied force over a distance, has units of energy. In fact, the notion that heat (http://scienceworld.wolfram.com/physics/Heat.html) is a form of energy (http://scienceworld.wolfram.com/physics/Energy.html) was one of the most important developments in classical physics and thermodynamics. Energy is related to power (http://scienceworld.wolfram.com/physics/Power.html) P emitted over a time t by http://scienceworld.wolfram.com/physics/eimg329.gif

Conservation of Energyhttp://scienceworld.wolfram.com/images/tealtab_topright.gif
http://scienceworld.wolfram.com/images/gradient-teal.gifhttp://scienceworld.wolfram.com/images/spacer.gifhttp://scienceworld.wolfram.com/images/spacer.gif
If the forces acting on a particle are conservative so that there exists a function http://scienceworld.wolfram.com/physics/cimg270.gif such that http://scienceworld.wolfram.com/physics/cimg271.gif

then the total energy http://scienceworld.wolfram.com/physics/cimg272.gif

given as the sum of kinetic energy (http://scienceworld.wolfram.com/physics/KineticEnergy.html) and potential energy (http://scienceworld.wolfram.com/physics/PotentialEnergy.html) is a constant.

Energy Densityhttp://scienceworld.wolfram.com/images/tealtab_topright.gif
http://scienceworld.wolfram.com/images/gradient-teal.gifhttp://scienceworld.wolfram.com/images/spacer.gifhttp://scienceworld.wolfram.com/images/spacer.gif Energy density is the amount of energy stored in a given system or region of space per unit volume, and is most commonly denoted u. It therefore has units of energy per length cubed.

Energy Fluxhttp://scienceworld.wolfram.com/images/tealtab_topright.gif
http://scienceworld.wolfram.com/images/gradient-teal.gifhttp://scienceworld.wolfram.com/images/spacer.gifhttp://scienceworld.wolfram.com/images/spacer.gif
http://scienceworld.wolfram.com/physics/eimg331.gif(1)



The mean energy flux (http://scienceworld.wolfram.com/physics/Flux.html) is http://scienceworld.wolfram.com/physics/eimg332.gif, also written as http://scienceworld.wolfram.com/physics/eimg333.gif and called I, the intensity (http://scienceworld.wolfram.com/physics/Intensity.html). For a traveling wave, http://scienceworld.wolfram.com/physics/eimg335.gif(2)




The unit of energy flux is 1 J m-2 s-1 = 1 kg s-3. For radiation, consider a half-plane filled with energy density (http://scienceworld.wolfram.com/physics/EnergyDensity.html) u, then http://scienceworld.wolfram.com/physics/eimg336.gif(3)


where c is the speed of light (http://scienceworld.wolfram.com/physics/SpeedofLight.html), http://scienceworld.wolfram.com/physics/eimg124.gif is the angle from the propagation axis, a is the radiation constant (http://scienceworld.wolfram.com/physics/RadiationConstant.html), T is the temperature (http://scienceworld.wolfram.com/physics/Temperature.html), and http://scienceworld.wolfram.com/physics/eimg30.gif is the Stefan-Boltzmann constant (http://scienceworld.wolfram.com/physics/Stefan-BoltzmannConstant.html)




http://scienceworld.wolfram.com/images/tealtab_topright.gif



http://scienceworld.wolfram.com/images/tealtab_topright.gif



Foot Pound


A unit of energy (http://scienceworld.wolfram.com/physics/Energy.html) equal to http://scienceworld.wolfram.com/physics/fimg176.gif http://scienceworld.wolfram.com/physics/fimg177.gif http://scienceworld.wolfram.com/physics/fimg178.gif

Heat



The first law of thermodynamics (http://scienceworld.wolfram.com/physics/FirstLawofThermodynamics.html) http://scienceworld.wolfram.com/physics/himg112.gif(1)


where http://scienceworld.wolfram.com/physics/himg113.gif is the heat change, dE is the energy change, http://scienceworld.wolfram.com/physics/himg115.gif is the work done, P is the pressure (http://scienceworld.wolfram.com/physics/Pressure.html), dV is the volume change, T is the temperature, and dS is the entropy (http://scienceworld.wolfram.com/physics/Entropy.html) change, can be written at constant volume as http://scienceworld.wolfram.com/physics/himg118.gifhttp://scienceworld.wolfram.com/physics/himg48.gifhttp://scienceworld.wolfram.com/physics/himg119.gif(2) http://scienceworld.wolfram.com/physics/himg48.gifhttp://scienceworld.wolfram.com/physics/himg120.gif http://scienceworld.wolfram.com/physics/himg48.gifhttp://scienceworld.wolfram.com/physics/himg121.gif(3) http://scienceworld.wolfram.com/physics/himg48.gifhttp://scienceworld.wolfram.com/physics/himg122.gif http://scienceworld.wolfram.com/physics/himg48.gifhttp://scienceworld.wolfram.com/physics/himg123.gif http://scienceworld.wolfram.com/physics/himg48.gifhttp://scienceworld.wolfram.com/physics/himg124.gif(4)

where http://scienceworld.wolfram.com/physics/himg125.gif is the heat capacity (http://scienceworld.wolfram.com/physics/HeatCapacity.html) at constant pressure, http://scienceworld.wolfram.com/physics/himg126.gif is the thermal expansion coefficient (http://scienceworld.wolfram.com/physics/ThermalExpansionCoefficient.html), and http://scienceworld.wolfram.com/physics/himg127.gif is the isothermal bulk modulus (http://scienceworld.wolfram.com/physics/IsothermalBulkModulus.html).

At constant pressure, http://scienceworld.wolfram.com/physics/himg128.gifhttp://scienceworld.wolfram.com/physics/himg48.gifhttp://scienceworld.wolfram.com/physics/himg129.gif(5) http://scienceworld.wolfram.com/physics/himg48.gifhttp://scienceworld.wolfram.com/physics/himg130.gif http://scienceworld.wolfram.com/physics/himg48.gifhttp://scienceworld.wolfram.com/physics/himg131.gif(6) http://scienceworld.wolfram.com/physics/himg48.gifhttp://scienceworld.wolfram.com/physics/himg132.gif (7) http://scienceworld.wolfram.com/physics/himg48.gifhttp://scienceworld.wolfram.com/physics/himg133.gif http://scienceworld.wolfram.com/physics/himg48.gifhttp://scienceworld.wolfram.com/physics/himg134.gif(8)

where http://scienceworld.wolfram.com/physics/himg135.gif is the heat capacity (http://scienceworld.wolfram.com/physics/HeatCapacity.html) at constant volume.

10/10.................

Second Law of Thermodynamics

The second law of thermodynamics prohibits the construction of a perpetual motion machine (http://scienceworld.wolfram.com/physics/PerpetualMotionMachine.html) "of the second kind." There are two usual statements of this law. Kelvin's (http://scienceworld.wolfram.com/biography/Kelvin.html) http://scienceworld.wolfram.com/images/crossrefs/biography.gif formulation states that it is impossible for a system operating in a cycle and in contact with one thermal reservoir to perform positive work in the surroundings. Clausius's (http://scienceworld.wolfram.com/biography/Clausius.html) http://scienceworld.wolfram.com/images/crossrefs/biography.gif formulation states that it is impossible for a system operating in a cycle to produce positive heat flow from a colder body to a hotter body.

Combined Law of Thermodynamics


For energy E, temperature T, pressure P, and volume V, http://scienceworld.wolfram.com/physics/cimg226.gif



Entropyhttp://scienceworld.wolfram.com/images/tealtab_topright.gif





Entropy is a measure of the disorder of a system, and is defined by http://scienceworld.wolfram.com/physics/eimg346.gif(1)



where http://scienceworld.wolfram.com/physics/eimg114.gif is the number of states (http://scienceworld.wolfram.com/physics/States.html) of a system. In terms of the partition function (http://scienceworld.wolfram.com/physics/PartitionFunction.html) Z, http://scienceworld.wolfram.com/physics/eimg348.gif(2)

Reversible Process


A reversible process is one in which the timescale is assumed to be so slow that every intermediate state deviates only infinitesimally from equilibrium (http://scienceworld.wolfram.com/physics/Equilibrium.html). Every intermediate state is exactly described by a set of macroscopic thermodynamic variables and may be assumed to be at equilibrium. Since every intermediate state is exactly known, the process may be reversed at an infinitesimally slow rate. This may be simply illustrated by imagining a cylinder with a frictionless piston on the top. Further imagine that there is a quantity of sand on top of the piston. A good approximation to a reversible process would be realized by removing the sand one grain at a time and carefully recording the thermodynamic variables (temperature and pressure in this case) after each grain of sand is removed. This would be a reversible expansion and one could individually return the grains of sand one at a time and reproduce each intermediate state exactly, thus reversing the transformation.
Equilibrium (http://scienceworld.wolfram.com/physics/topics/Equilibrium.html)http://scienceworld.wolfram.com/images/teal_downarrow.gif

Equilibrium Constanthttp://scienceworld.wolfram.com/images/tealtab_topright.gif




The equilibrium constant for a chemical reaction is given by http://scienceworld.wolfram.com/physics/eimg351.gif



where http://scienceworld.wolfram.com/physics/eimg352.gif is the Helmholtz free energy (http://scienceworld.wolfram.com/physics/HelmholtzFreeEnergy.html), k is the Stefan-Boltzmann constant (http://scienceworld.wolfram.com/physics/Stefan-BoltzmannConstant.html), and T is the temperature (http://scienceworld.wolfram.com/physics/Temperature.html)

Helmholtz Free Energyhttp://scienceworld.wolfram.com/images/tealtab_topright.gif




The Helmholtz free energy is defined by http://scienceworld.wolfram.com/physics/himg186.gif(1)




where E is the energy, T is the temperature (http://scienceworld.wolfram.com/physics/Temperature.html), and S is the entropy (http://scienceworld.wolfram.com/physics/Entropy.html). When a system changes its thermodynamic state, the change in Helmholtz free energy is therefore given by http://scienceworld.wolfram.com/physics/himg187.gif(2)




If T and V are constant, the (2) reduces to http://scienceworld.wolfram.com/physics/himg188.gif(3)




But the combined law of thermodynamics (http://scienceworld.wolfram.com/physics/CombinedLawofThermodynamics.html) states that http://scienceworld.wolfram.com/physics/himg189.gif(4)




and, since we have stipulated dV = 0, this becomes http://scienceworld.wolfram.com/physics/himg191.gif(5)




Therefore http://scienceworld.wolfram.com/physics/himg192.gif(6)




The Helmholtz free energy is intimately related to the equilibrium constant (http://scienceworld.wolfram.com/physics/EquilibriumConstant.html) at constant volume http://scienceworld.wolfram.com/physics/himg193.gif via http://scienceworld.wolfram.com/physics/himg194.gif(7)



where k is Boltzmann's constant (http://scienceworld.wolfram.com/physics/BoltzmannsConstant.html). A system with fixed external parameters in thermal contact with a heat reservoir (http://scienceworld.wolfram.com/physics/HeatReservoir.html) at equilibrium has a minimum Helmholtz free http://scienceworld.wolfram.com/physics/himg195.gifenergy, commonly denoted

Equilibrium Postulatehttp://scienceworld.wolfram.com/images/tealtab_topright.gif


An isolated system in equilibrium is equally likely to be in any of its accessible states


Mechanical Equilibrium

A system is said to be in mechanical equilibrium if http://scienceworld.wolfram.com/physics/mimg206.gif

where http://scienceworld.wolfram.com/physics/mimg207.gif is the applied force and http://scienceworld.wolfram.com/physics/mimg208.gif is the virtual displacement


Floating


Homogeneous spheres float stably in all possible orientations (Ulam 1960), but it has never been proved that no other homogeneous body shares this property (Gilbert 1991).
http://scienceworld.wolfram.com/physics/fimg148.gif
When the two above shapes have uniform density 0.5 they, like the uniform sphere of density 1, will float in a liquid in any orientation without tending to rotate (Mauldin 1982, Wells 1991, Gilbert 1991

Thermodynamic Lawshttp://scienceworld.wolfram.com/images/tealtab_topright.gif



0. If two systems are in thermal equilibrium with a third system, then they must be in thermal equilibrium with each other. 1. http://scienceworld.wolfram.com/physics/timg81.gif, where dE is the energy change, http://scienceworld.wolfram.com/physics/timg83.gif is the change in heat, dW is the work done, T is the temperature (http://scienceworld.wolfram.com/physics/Temperature.html), dS is the change in entropy (http://scienceworld.wolfram.com/physics/Entropy.html), P is the pressure (http://scienceworld.wolfram.com/physics/Pressure.html), and dV is the volume change. 2. The second law of thermodynamics prohibits the construction of a perpetual motion machine (http://scienceworld.wolfram.com/physics/PerpetualMotionMachine.html) of `the second kind.' A consequence is the result that http://scienceworld.wolfram.com/physics/timg87.gif. 3. As temperature (http://scienceworld.wolfram.com/physics/Temperature.html) goes to 0, the entropy (http://scienceworld.wolfram.com/physics/Entropy.html) S approaches a constant http://scienceworld.wolfram.com/physics/timg88.gif. Combining the first and second laws gives the combined law of thermodynamics (http://scienceworld.wolfram.com/physics/CombinedLawofThermodynamics.html)
http://scienceworld.wolfram.com/physics/timg89.gif

Third Law of Thermodynamics

As temperature (http://scienceworld.wolfram.com/physics/Temperature.html) goes to 0, the entropy (http://scienceworld.wolfram.com/physics/Entropy.html) S approaches a constant http://scienceworld.wolfram.com/physics/timg88.gif. Furthermore, it guarantees that the entropy (http://scienceworld.wolfram.com/physics/Entropy.html) of a pure, perfectly crystalline substance is 0 if the absolute temperature is 0.

Zeroth Law of Thermodynamicshttp://scienceworld.wolfram.com/images/tealtab_topright.gif

If two systems are in thermal equilibrium (http://scienceworld.wolfram.com/physics/ThermalEquilibrium.html) with a third system, then they must be in thermal equilibrium (http://scienceworld.wolfram.com/physics/ThermalEquilibrium.html) with each other.

Blackbody

A hypothetic body that completely absorbs all wavelengths of thermal radiation (http://scienceworld.wolfram.com/physics/ThermalRadiation.html) incident on it. Such bodies do not reflect light, and therefore appear black if their temperatures are low enough so as not to be self-luminous. All blackbodies heated to a given temperature emit thermal radiation (http://scienceworld.wolfram.com/physics/ThermalRadiation.html) with the same spectrum, as required by arguments of classical physics involving thermal equilibrium. However, the distribution of blackbody radiation (http://scienceworld.wolfram.com/physics/BlackbodyRadiation.html) as a function of wavelength, known as the Planck law (http://scienceworld.wolfram.com/physics/PlanckLaw.html), cannot be predicted using classical physics. This fact was the first motivating force behind the development of quantum mechanics (http://scienceworld.wolfram.com/physics/QuantumMechanics.html)

Blackbody Radiation

The thermal radiation (http://scienceworld.wolfram.com/physics/ThermalRadiation.html) emitted by a blackbody (http://scienceworld.wolfram.com/physics/Blackbody.html) heated to a given temperature (http://scienceworld.wolfram.com/physics/Temperature.html). All blackbodies heated to a given temperature emit thermal radiation (http://scienceworld.wolfram.com/physics/ThermalRadiation.html) with the same spectrum, known as the Planck law (http://scienceworld.wolfram.com/physics/PlanckLaw.html).

Blackbody Temperature
The effective temperature (http://scienceworld.wolfram.com/physics/Temperature.html) at which a blackbody (http://scienceworld.wolfram.com/physics/Blackbody.html) emits blackbody radiation (http://scienceworld.wolfram.com/physics/BlackbodyRadiation.html).

Plack Energ

http://scienceworld.wolfram.com/images/tealtab_topright.gif


The Planck energy is the average energy of an oscillator, http://scienceworld.wolfram.com/physics/pimg239.gif(1)


The Planck postulate (http://scienceworld.wolfram.com/physics/PlanckPostulate.html) states that http://scienceworld.wolfram.com/physics/pimg240.gif(2)


where n is a nonnegative integer, h is Planck's constant (http://scienceworld.wolfram.com/physics/PlancksConstant.html), and http://scienceworld.wolfram.com/physics/pimg224.gif is the frequency of radiation. Maxwell-Boltzmann statistics (http://scienceworld.wolfram.com/physics/Maxwell-BoltzmannStatistics.html) give http://scienceworld.wolfram.com/physics/pimg241.gif(3)


where C is a constant, k is Boltzmann's constant (http://scienceworld.wolfram.com/physics/BoltzmannsConstant.html), and T is the temperature (http://scienceworld.wolfram.com/physics/Temperature.html). Plugging in, http://scienceworld.wolfram.com/physics/pimg242.gif(4)

Planck Intensity Densityhttp://scienceworld.wolfram.com/images/tealtab_topright.gif
http://scienceworld.wolfram.com/images/gradient-teal.gif

In terms of frequency, the energy flux from blackbody radiation is given by http://scienceworld.wolfram.com/physics/pimg243.gifhttp://scienceworld.wolfram.com/physics/pimg15.gifhttp://scienceworld.wolfram.com/physics/pimg244.gif http://scienceworld.wolfram.com/physics/pimg15.gifhttp://scienceworld.wolfram.com/physics/pimg245.gif http://scienceworld.wolfram.com/physics/pimg15.gifhttp://scienceworld.wolfram.com/physics/pimg246.gif(1)

where http://scienceworld.wolfram.com/physics/pimg247.gif is the average energy density, http://scienceworld.wolfram.com/physics/pimg248.gif is Planck energy (http://scienceworld.wolfram.com/physics/PlanckEnergy.html), N is the number density of oscillators, h is Planck's constant (http://scienceworld.wolfram.com/physics/PlancksConstant.html), k is Boltzmann's constant (http://scienceworld.wolfram.com/physics/BoltzmannsConstant.html), and T is the temperature (http://scienceworld.wolfram.com/physics/Temperature.html). Here, http://scienceworld.wolfram.com/physics/pimg249.gif(2)


is the number of cells per unit phase space. The factor of 2 must be added since two electrons with opposite spins may occupy the same element of phase space. The momentum (http://scienceworld.wolfram.com/physics/Momentum.html) of a photon (http://scienceworld.wolfram.com/physics/Photon.html) is given by http://scienceworld.wolfram.com/physics/pimg250.gif(3)


so http://scienceworld.wolfram.com/physics/pimg251.gif(4)


and http://scienceworld.wolfram.com/physics/pimg252.gif(5)


where http://scienceworld.wolfram.com/physics/pimg206.gif is an element of solid angle. Plugging in, http://scienceworld.wolfram.com/physics/pimg243.gifhttp://scienceworld.wolfram.com/physics/pimg15.gifhttp://scienceworld.wolfram.com/physics/pimg253.gif http://scienceworld.wolfram.com/physics/pimg15.gifhttp://scienceworld.wolfram.com/physics/pimg254.gif

Planck Law


Planck Lawhttp://scienceworld.wolfram.com/images/tealtab_topright.gif
http://scienceworld.wolfram.com/images/gradient-teal.gifhttp://scienceworld.wolfram.com/images/spacer.gifhttp://scienceworld.wolfram.com/images/spacer.gif
http://scienceworld.wolfram.com/physics/pimg255.gif

The Planck law gives the intensity radiated by a blackbody as a function of frequency (or wavelength). Let a blackbody (http://scienceworld.wolfram.com/physics/Blackbody.html) have temperature (http://scienceworld.wolfram.com/physics/Temperature.html) T. Let http://scienceworld.wolfram.com/physics/pimg256.gif be the energy density per unit solid angle so that http://scienceworld.wolfram.com/physics/pimg257.gif(1)

then the blackbody radiates at a frequency http://scienceworld.wolfram.com/physics/pimg224.gif with spectral energy density http://scienceworld.wolfram.com/physics/pimg258.gif(2)

where h is Planck's constant (http://scienceworld.wolfram.com/physics/PlancksConstant.html), c is the speed of light (http://scienceworld.wolfram.com/physics/SpeedofLight.html), and k is Boltzmann's constant (http://scienceworld.wolfram.com/physics/BoltzmannsConstant.html) (Rybicki and Lightman 1979, p. 21).

وسنكمل ان شاء الله

يتبع

جزاك الله كل خير

Planck Occupancy


In terms of frequency, http://scienceworld.wolfram.com/physics/pimg263.gif(1)


and in terms of wavelength http://scienceworld.wolfram.com/physics/pimg264.gif

Planck Postulate



Planck (http://scienceworld.wolfram.com/biography/Planck.html) http://scienceworld.wolfram.com/images/crossrefs/biography.gif postulated that the energy of oscillators in a blackbody (http://scienceworld.wolfram.com/physics/Blackbody.html) is quantized by http://scienceworld.wolfram.com/physics/pimg265.gif(1)


where n = 1, 2, 3, ..., h is Planck's constant (http://scienceworld.wolfram.com/physics/PlancksConstant.html), and http://scienceworld.wolfram.com/physics/pimg224.gif is the frequency, and used this postulate in his derivation of the Planck law (http://scienceworld.wolfram.com/physics/PlanckLaw.html) of blackbody radiation. In fact, electromagnetic radiation is itself quantized, coming in packets known as photons (http://scienceworld.wolfram.com/physics/Photon.html) and having energy http://scienceworld.wolfram.com/physics/pimg237.gif(2)

In the other hand, the energy of state n of quantum mechanical simple harmonic oscillator (http://scienceworld.wolfram.com/physics/SimpleHarmonicOscillatorQuantumMechanical.html) is actually given by the slightly modified form http://scienceworld.wolfram.com/physics/pimg267.gif(3)

Radiation Constanthttp://scienceworld.wolfram.com/images/tealtab_topright.gif



The constant related to the total energy radiated by a blackbody (http://scienceworld.wolfram.com/physics/Blackbody.html) (i.e., the Stefan-Boltzmann law (http://scienceworld.wolfram.com/physics/Stefan-BoltzmannLaw.html)), and defined as http://scienceworld.wolfram.com/physics/rimg24.gifhttp://scienceworld.wolfram.com/physics/rimg16.gifhttp://scienceworld.wolfram.com/physics/rimg25.gif http://scienceworld.wolfram.com/physics/rimg26.gifhttp://scienceworld.wolfram.com/physics/rimg27.gif

where http://scienceworld.wolfram.com/physics/rimg28.gif is the Stefan-Boltzmann constant (http://scienceworld.wolfram.com/physics/Stefan-BoltzmannConstant.html), c is the speed of light (http://scienceworld.wolfram.com/physics/SpeedofLight.html), k is Boltzmann's constant (http://scienceworld.wolfram.com/physics/BoltzmannsConstant.html), and h is Planck's constant (http://scienceworld.wolfram.com/physics/PlancksConstant.html). Numerically, http://scienceworld.wolfram.com/physics/rimg24.gifhttp://scienceworld.wolfram.com/physics/rimg26.gifhttp://scienceworld.wolfram.com/physics/rimg31.gif http://scienceworld.wolfram.com/physics/rimg26.gifhttp://scienceworld.wolfram.com/physics/rimg32.gif

Radiometer Equationhttp://scienceworld.wolfram.com/images/tealtab_topright.gif


http://scienceworld.wolfram.com/physics/rimg109.gif



where http://scienceworld.wolfram.com/physics/rimg110.gif is the root-mean-square noise, http://scienceworld.wolfram.com/physics/rimg111.gif is a factor http://scienceworld.wolfram.com/physics/rimg112.gif, B is the bandwidth, and http://scienceworld.wolfram.com/physics/rimg91.gif is the integration time.

Rayleigh-Jeans Law



http://scienceworld.wolfram.com/physics/rimg141.gif

A classical law approximately describing the intensity of radiation emitted by a blackbody (http://scienceworld.wolfram.com/physics/Blackbody.html), derived by Rayleigh and Jeans by counting the number of standing wave modes in an enclosure. It corresponds to the Planck law (http://scienceworld.wolfram.com/physics/PlanckLaw.html) in the case of small frequencies, in which case http://scienceworld.wolfram.com/physics/rimg142.gif allows the approximation http://scienceworld.wolfram.com/physics/rimg143.gif(1)


Plugging this into the Planck law (http://scienceworld.wolfram.com/physics/PlanckLaw.html) gives http://scienceworld.wolfram.com/physics/rimg144.gifhttp://scienceworld.wolfram.com/physics/rimg145.gifhttp://scienceworld.wolfram.com/physics/rimg146.gif http://scienceworld.wolfram.com/physics/rimg26.gifhttp://scienceworld.wolfram.com/physics/rimg147.gif(2)

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