Talk:Paschen's law

Trojancowboy (talk) 03:05, 23 December 2010 (UTC) This article needs a graph of the equation and I don't know how to do it.Trojancowboy (talk) 02:32, 25 March 2008 (UTC)

The equation for air seems to be almost a factor of two different from the first reference (High Voltage Experimenters Handbook). Also there is no provision for temperature effects. Can anyone confirm whether reference is correct or this article is correct? —Preceding unsigned comment added by 24.62.110.98 (talk) 10:07, 17 March 2009 (UTC)

I think that it should say (for air) a = 43.6E6 V/(atm-m) and b = 12.8. This will get the correct 327 V voltage breakdown at 7.5E-6 atm-um. I was unable to find an accurate source that lists the full equation with the values. 66.112.231.201 (talk) 04:10, 30 April 2009 (UTC)

The article states that "For air at STP, the voltage needed to arc a 1 meter gap is about 3.4 MV" but if you plug in 1 meter into the equation: ( 43600000 * 101300 *1)   /  ( ln(101300 * 1 ) + 12.8 ) you get 1.81583*10^11 volts, which is crazy. 101300 is in Pa, d is in meters. ??? — Preceding unsigned comment added by 24.227.215.162 (talk) 19:21, 4 June 2012 (UTC)

Pressure is a function of temperature, from the ideal gas law. 66.112.231.201 (talk) 03:33, 30 April 2009 (UTC)

Maybe the first formula would be more readable as:


 * $$V=\frac{apd}{\ln(bpd)}$$.

Where V is the breakdown voltage, p is the pressure, d is the gap distance. The constants a and b depend upon the composition of the gas. For air at standard atmospheric pressure of 101 kPa, a = 43.6×106 V/(atm·m) and b = 3.62x105/(atm·m). — Preceding unsigned comment added by 85.81.102.102 (talk) 21:02, 11 July 2011 (UTC)

The formula would not only be more readable, it would actually be correct. In the current form, it does not make sense, since 'pd' has a unit, so one cannot take the logarithm from this value. Fruehling42 (talk) 19:54, 6 March 2012 (UTC)

Consistency
In the section "Paschen curve", the description repeatedly states 7.5 mm, whilst in the explanation (2 paragraphs below), 7.5 um is mentioned. I don't have the time to check which one is correct, but this inconsistency should be weeded out! --83.65.160.242 (talk) 08:13, 3 August 2011 (UTC)
 * Not inconsistent - one is at 0.001 atmospheres, the other at 1 atmosphere. --Wtshymanski (talk) 13:44, 3 August 2011 (UTC)
 * This should be made clear. Currently it is not - I had the exact same confusion.18.38.2.39 (talk) 17:53, 28 October 2011 (UTC)
 * ...For example, at a pressure of 10-3 atmospheres, the distance for minimum breakdown voltage is about 7.5 mm. ..., and This is 327 V in air at standard atmospheric pressure at a distance of 7.5 µm. How would you suggest clarifying this? The whole article is talking about the effect of pressure on minimum breakdwon voltage and gaps, I don't see how to change this. --Wtshymanski (talk) 17:58, 28 October 2011 (UTC)

Units are inconsistent on at least equations 14 and 15. The units in the exponent of eq. 14 do not all cancel. Also, a dimensional analysis of eq. 15 does not yield volts. Woops! — Preceding unsigned comment added by 129.123.197.35 (talk) 23:38, 15 August 2012 (UTC)

The problem is actually Eq. 8, which defines $$L$$. The product $$Lpd$$ is unitless, which should make the units for Eq. 14 & 15 work. I will fix Eq. 8.Cfn137 (talk) 17:12, 15 October 2012 (UTC)

better equation and easier explanation
The page could do with a better writeup. It took me several minutes of thinking to realize from the equation that, regardless of the pressure and distance, there is a certain absolute minimum voltage required to cause a spark that is a constant. What I mean is, if I have two objects with a variety of distances to one another, at a given pressure, then the formation of a spark from any point to any other point (considering all possible distances) requires that minimum voltage. As noted by other comments above, there is also a units inconsistency.

I think the equation would be much better written out as:
 * $$ V = \frac{V_{\rm min} pd/c}{1+\ln(pd/c)} $$

Advantages:
 * It is no longer necessary to demand certain units for pd, since we will naturally compensate them when dividing by c.
 * The value Vmin is the minimum voltage required to cause a spark under any possible conditions (at any pressure, at any distance), whereas V is the minimum voltage required to cause a spark under specific conditions (at a certain pressure and distance).
 * The value of c is the critical value of pd where V is lowest, i.e., where V falls to Vmin.

The relationships between the different constants are of course:
 * $$c = e^{1-b} \times (1\, \mathrm{atm\, m}), \quad V_{\rm min} = ac $$

--Nanite (talk) 10:51, 4 September 2013 (UTC)

It isn't really a unit inconsistency given that it is equivalent through log identities. Maybe just not immediately obvious to the casual reader. But this form of the equation is much more elegant as it is written in a way the emphasises the key physical parameters in the relationship. This would help clarify for the reader that there is a Vmin located at some pd value related to the value of c. It avoids the extra leap of understanding taken in the article involving taking a derivative w.r.t. pd. Updating the wiki entry to the your above equation would be very beneficial to the reader. The only sticking point is whether or not you can reference this back to textbooks or academic papers that use this as a standard form. We're not supposed to invent conventions on wikipedia, just faithfully bring together the sum of all knowledge as it stands. Fincle (talk) 23:38, 7 April 2014 (UTC)

Fincle is wrong and Nanite is right
The edit should be made in a way that clarifies and explicates in text following the historical explanation. That would mollify Fincle's concern about 'invention'.

I don't come to an encyclopedia looking for a thoughtless clerical compendium of human knowledge devoid of any real understanding by the author(s). I come looking to learn what is unambiguously known, and as such, I seek clarity of exposition that is faithful to truth.

Arguably, all expressions in an encylopedia are original authorship. The criterion for acceptability is that the abstract content be a re-expression of the consensus others have arrived at elsewhere in original and secondary sources. This does not preclude clarity.

To put a point on it, I challenge Fincle to understand the content of early mathematical papers using only the notation of those papers. Doing so requires special expertise and experience.

As for 'log identities' I will say this. The argument of a logarithm should always be expressed as a unitless quantity. The presence of a logarithmic relation in a physical system implies a dimensionless invariant that characterizes the system. This should always be highlighted for the sake of clarity. That some practitioners failed to do this is no excuse for not correcting their oversight. Such a correction is in no way original; neither is it an 'invention' of a new convention. It is a courtesy to the reader, and lets the reader know you do not wish to waste his or her time with academic pomposity.

I would make the edits myself, but really, I have grown so weary of fighting intransigently stubborn and bureaucratic wikipedians. Do you really want to make wikipedia better? Then serve your audience: people who desire to learn and understand. In order to do that, you have to be infected with that desire yourself. Otherwise you are just a stuffy clerk.

Wrong curve
I moved the following comment by from the article here: Curve for Nitrogen is wrong http://neon.dpp.fmph.uniba.sk/workgroup/media/documents/microdischarge_1.pdf &mdash;&thinsp; H HHIPPO  19:08, 3 April 2014 (UTC)

This isn't actually a peer reviewed paper. It claims its from the an institution in the Solvak Republic. You simply can't alter content of a wiki page on the basis of a self published paper. It could have come from anyone claiming to be from this institution. We don't even know of the credentials of the institution. This paper is probably best disregarded until it finds its way into an international journal. Fincle (talk) 00:40, 4 April 2014 (UTC)

Typo in defining first Townshend coefficient?
The article states, "Per length of path $$x$$ a number of $$\alpha$$ ionizations will occur." Shouldn't this read "a number $$\alpha$$ of ionizations will occur"? ᛭ LokiClock (talk) 06:01, 2 August 2015 (UTC)

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Unclear
The text mixes "B" for most of the equations, and "b" for the minimum, and "b" is never defined. From the Talk page, it seems they might be the same thing. In the article it is a mystery. Also, that section needs citations. — Preceding unsigned comment added by DrKN1 (talk • contribs) 22:10, 28 March 2017 (UTC)

Equations do not match cited source material
The Townsend equations do not include beta, which is present throughout both of Townsend's books, and does include gamma, which is not visible so far as I have looked in that material either. Also I can't find any equation matching the final results given here in the books, it must need to be derived. This derivation should be made explicit as it is not included in the source material. Mr. HelloBye (talk) 20:22, 2 December 2022 (UTC)