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| [[Image:RWP-comparison.svg|thumb|300px|Comparison of Rayleigh–Jeans law with [[Wien approximation]] and [[Planck's law]], for a body of 8 mK [[temperature]].]]
| | "Why does my computer keep freezing up?" I was asked by a great deal of persons the cause of their pc freeze issues. And I am fed up with spending much time inside answering the query time and time again. This post is to tell we the real cause of your PC Freezes.<br><br>Carry out window's program restore. It is truly important to do this because it removes wrong changes which have taken place in the system. Some of the mistakes outcome from inability of your program to create restore point frequently.<br><br>If you compare registry products we require a rapidly acting registry cleaning. It's no advantageous spending hours and the PC waiting for your registry cleaning to complete its task. We wish your cleaner to complete its task in minutes.<br><br>Always see with it which we have installed antivirus, anti-spyware and anti-adware programs plus have them updated on a regular basis. This can help stop windows XP running slow.<br><br>The [http://bestregistrycleanerfix.com/registry-reviver registry reviver] should come as standard with a back up plus restore center. This ought to be an effortless to apply process.That signifies which in the event you encounter a problem with the PC following utilizing a registry cleaning you are able to merely restore your settings.<br><br>The key reason why I could not make my PC run faster was the system registry and it being fragmented. So software to defragment or clean the registry are required. Such software are called registry products. Like all other software, there are paid ones plus free ones with their advantages plus disadvantages. To choose amongst the two is the user's choice.<br><br>It is important that you remove obsolete registry entries from a program on a regular basis, if you would like a system to run quicker, which is. If you don't keep the registry clean, a time comes when the program can stop working altogether. Then, your only choice will be to reformat the hard drive and begin over!<br><br>Another significant program you'll wish To get is a registry cleaner. The registry is a huge list of everything installed on your computer, and Windows references it whenever it opens a program or utilizes a device attached to the computer. When you delete a system, its registry entry could furthermore be deleted, but occasionally it's not. A registry cleaner may receive rid of these old entries so Windows will search the registry quicker. It equally deletes or corrects any entries that viruses have corrupted. |
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| In [[physics]], the '''Rayleigh–Jeans law''' attempts to describe the [[spectral radiance]] of [[electromagnetic radiation]] at all [[wavelengths]] from a [[black body]] at a given temperature through classical arguments. For wavelength ''λ'', it is:
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| :<math>B_\lambda(T) = \frac{2 c k T}{\lambda^4},</math>
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| where ''c'' is the [[speed of light]], ''k'' is the [[Boltzmann constant]] and ''T'' is the [[temperature]] in [[kelvin]]s. For [[frequency]] ''ν'', the expression is instead
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| :<math>B_\nu(T) = \frac{2 \nu^2 k T}{c^2}.</math>
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| The Rayleigh–Jeans law agrees with experimental results at large wavelengths (or, equivalently, low frequencies) but strongly disagrees at short wavelengths (or high frequencies). This inconsistency between observations and the predictions of [[classical physics]] is commonly known as the [[ultraviolet catastrophe]],<ref>''Astronomy: A Physical Perspective'', Mark L. Kutner pp. 15</ref><ref>''Radiative Processes in Astrophysics'', Rybicki and Lightman pp. 20–28</ref> and its resolution was a foundational aspect of the development of [[quantum mechanics]] in the early 20th century.
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| ==Historical development==
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| In 1900, the British physicist [[John Strutt, 3rd Baron Rayleigh|Lord Rayleigh]] derived the ''λ''<sup>−4</sup> dependence of the Rayleigh–Jeans law based on classical physical arguments.<ref>''Astronomy: A Physical Perspective'', Mark L. Kutner pp. 15</ref> A more complete derivation, which included the proportionality constant, was presented by Rayleigh and Sir [[James Jeans]] in 1905. The Rayleigh–Jeans law revealed an important error in physics theory of the time. The law predicted an energy output that diverges towards [[Infinity#Physics|infinity]] as wavelength approaches zero (as frequency tends to infinity) and measurements of energy output at short wavelengths disagreed with this prediction.
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| ==Comparison to Planck's law==
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| In 1900 [[Max Planck]] empirically obtained an expression for [[black-body radiation]] expressed in terms of wavelength {{nowrap|''λ'' {{=}} ''c''/''ν''}} ([[Planck's law]]):
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| :<math>B_\lambda(T) = \frac{2 h c^2}{\lambda^5}~\frac{1}{e^\frac{hc}{\lambda kT}-1},</math>
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| where ''h'' is the [[Planck constant]] and ''k'' the [[Boltzmann constant]]. The Planck law does not suffer from an ultraviolet catastrophe, and agrees well with the experimental data, but its full significance (which ultimately led to quantum theory) was only appreciated several years later. Since,
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| :<math>e^x = 1 + x + {x^2 \over 2!} + {x^3 \over 3!} + \cdots. </math>
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| then in the limit of very high temperatures or long wavelengths, the term in the exponential becomes small, and the exponential is well approximated with the [[Taylor series|Taylor polynomial's]] first-order term,
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| :<math>e^{\frac{hc}{\lambda kT}} \approx 1 + \frac{hc}{\lambda kT}.</math>
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| So,
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| :<math>\frac{1}{e^\frac{hc}{\lambda kT}-1} \approx \frac{1}{\frac{hc}{\lambda kT}} = \frac{\lambda kT}{hc}.</math>
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| This results in Planck's blackbody formula reducing to
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| :<math>B_{\lambda}(T) = \frac{2ckT}{\lambda^4},</math>
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| which is identical to the classically derived Rayleigh–Jeans expression. | |
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| The same argument can be applied to the blackbody radiation expressed in terms of frequency {{nowrap|''ν'' {{=}} ''c''/''λ''}}. In the limit of small frequencies, that is <math> h \nu \ll kT </math>,
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| :<math>B_\nu(T) = \frac{2h\nu^3/c^2}{e^\frac{h\nu}{kT} - 1} \approx \frac{2h\nu^3}{c^2} \cdot \frac{kT}{h\nu} = \frac{2 \nu^2 kT}{c^2}.</math>
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| This last expression is the Rayleigh–Jeans law in the limit of small frequencies.
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| ==Consistency of frequency and wavelength dependent expressions==
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| When comparing the frequency and wavelength dependent expressions of the Rayleigh–Jeans law it is important to remember that
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| :<math>B_{\lambda}(T) \neq B_{\nu}(T)</math>
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| because <math>B_{\lambda}(T)</math> has units of energy emitted per unit time per unit area of emitting surface, per unit solid angle, '''per unit wavelength''', whereas <math>B_{\nu}(T)</math> has units of energy emitted per unit time per unit area of emitting surface, per unit solid angle, '''per unit frequency'''. To be consistent, we must use the equality
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| :<math>B_{\lambda} \, d\lambda = B_{\nu} \, d\nu</math>
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| where both sides now have units of energy emitted per unit time per unit area of emitting surface, per unit solid angle.
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| Starting with the Rayleigh–Jeans law in terms of wavelength we get
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| :<math>B_{\lambda}(T) = B_{\nu}(T) \times \frac{d\nu}{d\lambda}</math>
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| where
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| :<math>\frac{d\nu}{d\lambda} = \frac{d}{d\lambda}\left(\frac{c}{\lambda}\right) = -\frac{c}{\lambda^2}</math>.
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| This leads us to find:
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| :<math>B_{\lambda}(T) = \frac{2kT\left( \frac{c}{\lambda}\right)^2}{c^2} \times \frac{c}{\lambda^2} = \frac{2ckT}{\lambda^4}</math>.
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| ==Other forms of Rayleigh–Jeans law==
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| Depending on the application, the Planck Function can be expressed in 3 different forms. The first involves energy emitted per unit time per unit area of emitting surface, per unit solid angle, per unit frequency. In this form, the Planck Function and associated Rayleigh–Jeans limits are given by
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| :<math>B_\lambda(T) = \frac{2 c^2}{\lambda^5}~\frac{h}{e^\frac{hc}{\lambda kT}-1} \approx \frac{2c kT}{\lambda^4}</math>
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| or
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| :<math>B_\nu(T) = \frac{2h\nu^2/c^2}{e^\frac{h\nu}{kT} - 1} \approx \frac{2kT\nu^2}{c^2}</math>
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| Alternatively, Planck's law can be written as an expression <math>u(\nu,T) = \pi I(\nu,T)</math> for emitted power integrated over all solid angles. In this form, the Planck Function and associated Rayleigh–Jeans limits are given by
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| :<math>u(\lambda,T) = \frac{2\pi c^2}{\lambda^5}~\frac{h}{e^\frac{hc}{\lambda kT}-1} \approx \frac{2\pi ckT}{\lambda^4}</math>
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| or
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| :<math>u(\nu,T) = \frac{2\pi h\nu^2/c^2}{e^\frac{h\nu}{kT} - 1} \approx \frac{2 \pi kT\nu^2}{c^2}</math>
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| In other cases, Planck's Law is written as <math>\rho(\nu,T) = \frac{4\pi}{c} I(\nu,T)</math> for energy per unit volume (energy density). In this form, the Planck Function and associated Rayleigh–Jeans limits are given by
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| :<math>\rho(\lambda,T) = \frac{8 \pi c}{\lambda^5}~\frac{h}{e^\frac{hc}{\lambda kT}-1} \approx \frac{8\pi kT}{\lambda^4}</math>
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| or | |
| :<math>\rho(\nu,T) = \frac{8\pi h\nu^3/c^3}{e^\frac{h\nu}{kT} - 1} \approx \frac{8 \pi kT\nu^2}{c^3}</math>
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| ==See also==
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| * [[Stefan–Boltzmann law]]
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| * [[Wien's displacement law]]
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| * [[Sakuma–Hattori equation]]
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| ==References==
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| <references/>
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| ==External links==
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| * [http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/rayj.html Derivation at HyperPhysics]
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| {{DEFAULTSORT:Rayleigh-Jeans law}}
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| [[Category:Foundational quantum physics]]
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"Why does my computer keep freezing up?" I was asked by a great deal of persons the cause of their pc freeze issues. And I am fed up with spending much time inside answering the query time and time again. This post is to tell we the real cause of your PC Freezes.
Carry out window's program restore. It is truly important to do this because it removes wrong changes which have taken place in the system. Some of the mistakes outcome from inability of your program to create restore point frequently.
If you compare registry products we require a rapidly acting registry cleaning. It's no advantageous spending hours and the PC waiting for your registry cleaning to complete its task. We wish your cleaner to complete its task in minutes.
Always see with it which we have installed antivirus, anti-spyware and anti-adware programs plus have them updated on a regular basis. This can help stop windows XP running slow.
The registry reviver should come as standard with a back up plus restore center. This ought to be an effortless to apply process.That signifies which in the event you encounter a problem with the PC following utilizing a registry cleaning you are able to merely restore your settings.
The key reason why I could not make my PC run faster was the system registry and it being fragmented. So software to defragment or clean the registry are required. Such software are called registry products. Like all other software, there are paid ones plus free ones with their advantages plus disadvantages. To choose amongst the two is the user's choice.
It is important that you remove obsolete registry entries from a program on a regular basis, if you would like a system to run quicker, which is. If you don't keep the registry clean, a time comes when the program can stop working altogether. Then, your only choice will be to reformat the hard drive and begin over!
Another significant program you'll wish To get is a registry cleaner. The registry is a huge list of everything installed on your computer, and Windows references it whenever it opens a program or utilizes a device attached to the computer. When you delete a system, its registry entry could furthermore be deleted, but occasionally it's not. A registry cleaner may receive rid of these old entries so Windows will search the registry quicker. It equally deletes or corrects any entries that viruses have corrupted.