Amplitude versus offset - Revision history

en>Yus.Ivanov: Shuey (1985) formula had a mistake in curvature term

2014-12-05T12:36:23Z

Shuey (1985) formula had a mistake in curvature term

← Older revision		Revision as of 14:36, 5 December 2014
Line 1:		Line 1:
	~~{{Refimprove\|date=December 2009}}~~

	'''Root-mean-square speed''' is the measure of the [[speed]] of particles in a gas that is most convenient for problem solving within the [[kinetic theory]] of gases. It is defined as the square root of the average velocity-squared of the molecules in a gas. It is given by the formula<ref>
	~~{{cite book~~
	~~\| title = College Physics, Volume 1~~
	~~\| edition = 9th~~
	~~\| author = Raymond A. Serway, Jerry S. Faughn, and Chris Vuille~~
	~~\| publisher = 9780840068484~~
	~~\| year = 2011~~
	~~\| isbn =~~
	~~\| page = 352~~
	~~\| url = http://books.google.com/books?id=HLxV-IKYO5IC&pg=PA352~~
	~~}}</ref>~~

	~~:<math>v_\mathrm{rms} = \sqrt {{3RT}\over{M_m}}</math>~~		Luke Bryan is usually a celebrity within the generating and the vocation progress 1st second to his third theatre record, And [http://lukebryantickets.citizenswebcasting.com concert tickets for sale] , is definitely the resistant. He burst open on the scene in 2013 together with his special mix of straight down-home convenience, movie superstar excellent looks and words, [http://www.netpaw.org luke bryan tour 2014 tickets] is set t in a major way. The new record Top around the region graph or chart and #2 in the burst graphs, creating it the next top debut during that time of 2011 to get a region designer. <br><br>The boy of the , knows determination and dedication are key elements with regards to a prosperous profession- . His 1st recording, Stay Me, produced the best hits “All My Buddies “Country and Say” Gentleman,” whilst his effort, Doin’ Point, found the performer-3 directly No. 2 men and women: More Getting in touch with Is a Excellent Point.”<br><br>While in the slip of 2012, Concert tour: Bryan And which had a remarkable list of , such as Metropolitan. “It’s much like you are acquiring a authorization to travel to another level, states individuals designers that were a part of the Concertsover in a bigger measure of designers.” It wrapped as among the best trips within its ten-calendar year record.<br><br>My site :: luke bryan 2014 tour schedule ([http://okkyunglee.com okkyunglee.com])

	~~where ''v''<sub>rms</sub>~~ is the ~~[[root mean square]] of~~ the ~~speed in meters per~~ second, ~~''M<sub>m<~~/~~sub>'' is the [[molar mass]] of the gas in kilograms per mole, ''R'' is the [[molar gas constant]~~], ~~and ''T''~~ is the ~~[[temperature]] in [[kelvin]]~~. ~~Although~~ the ~~molecules~~ in ~~a sample~~ of ~~gas have an average kinetic energy (~~and ~~therefore an average speed) the individual molecules move at various speeds and they stop and change direction according to the law of density measurements and isolation~~, i.e. ~~they exhibit~~ a distribution of speeds. Some move fast, others relatively slowly. Collisions change individual molecular speeds but the distribution of speeds remains the same. This equation is derived from kinetic theory of gases using [[Maxwell–Boltzmann distribution]] function. The ~~higher~~ the ~~temperature, the greater the mean velocity will be. This works well for both nearly ideal, atomic gases like [[helium]]~~ and ~~for [[Molecule\|molecular gas]]es like diatomic [[oxygen]]. This is because despite the larger internal energy in many molecules (compared to that for an atom), 3''RT''/~~2 ~~is still the mean [[Translation (physics)\|translational]] [[kinetic energy\|kinetic]] energy.~~
	~~This can also be written~~ in ~~terms of~~ the ~~[[Boltzmann constant]] (''k'') as~~

	~~:<math>v_\mathrm{rms} = \sqrt {{3kT}\over{m}}</math>~~

	~~where ''m'' is~~ the ~~mass~~ of ~~one molecule of the gas~~.

	~~This can be derived with energy methods:~~

	:<~~math~~>~~E_\mathrm{k} = {{3}\over{2}}nRT = \frac{3}{2}NkT~~<~~/math~~>
	~~where ''E''<sub>k</sub> is~~ the ~~[[kinetic energy]]~~ and ~~''N'' is the number of gas molecules~~.
	~~:<math>E_\mathrm{k~~,~~molecule} = {{1}\over{2}}mv^2</math>~~
	~~Given that ''v''<sup>2</sup> ignores direction~~, ~~it is logical to assume that~~ the ~~formula can be extended to the entire sample~~, ~~replacing ''m'' with the entire sample's mass~~, ~~equal to~~ the ~~molar mass times the number of moles ''n'' yielding~~
	~~:<math>{{1}\over{~~2~~}}nMv^2 = E_\mathrm{k}</math>~~
	~~Therefore~~
	:<~~math~~>~~v_\mathrm{rms} = \sqrt {{2E_\mathrm{k}}\over{m}}~~<~~/math~~>
	~~which is equivalent.~~

	~~The same result is obtained by solving~~ the ~~[[Gaussian integral]] containing the [[Maxwell speed distribution]]~~, ~~''p''(''v'')~~:
	~~<!-- The \~~,~~\! is~~ to ~~keep~~ the ~~formula rendered as PNG instead~~ of ~~HTML~~. ~~Please don't remove it~~.~~-->~~
	:<~~math~~>~~v_\mathrm{rms} = \sqrt{\int_{0}^{\infty} v^2\ p(v)dv}\,\!~~ <~~/math~~>
	::~~<math> = \sqrt{\int_{0}^{\infty} 4 \pi \left~~ (~~\frac{m}{2 \pi k T} \right )^\frac{3}{2} v^4\ e^{-\frac{v^{2}m}{2kT}}dv}\,\!</math>~~
	::~~<math> = \sqrt{4 \pi \left (\frac{m}{2 \pi k T} \right )^\frac{3}{2} \frac{3}{8} \pi^{\frac{1}{2}} \left( \frac{2kT}{m}\right)^{\frac{5}{2}}}\,\!<~~/~~math>~~
	~~::<math> = \sqrt{\frac{3kT}{m}}<~~/~~math>~~

	~~==References==~~

	~~{{reflist}}~~

	~~{{DEFAULTSORT:Root Mean Square Speed}}~~
	~~[[Category:Gases]~~]

en>Kwinkunks: /* Zoeppritz equations */ see main article

2013-09-15T13:54:42Z

Zoeppritz equations: see main article

← Older revision		Revision as of 15:54, 15 September 2013
Line 1:		Line 1:
	~~Hi there~~, ~~I am Alyson Pomerleau~~ and ~~I believe it seems fairly great when you say it~~. ~~Office supervising~~ is ~~what she does for a residing~~. ~~For~~ a ~~whilst I've been in Alaska but I will~~ have to move ~~in a year or two~~. The ~~preferred pastime~~ for ~~him~~ and ~~his children~~ is to ~~play lacross and he would never give it up~~.<br><br>~~Here~~ is ~~my site;~~ [~~http~~://~~www~~.~~acorntown~~.~~com~~/~~space.php?uid~~=~~763416&do~~=~~blog&id~~=~~738203 love psychic~~]		{{Refimprove\|date=December 2009}}

			'''Root-mean-square speed''' is the measure of the [[speed]] of particles in a gas that is most convenient for problem solving within the [[kinetic theory]] of gases. It is defined as the square root of the average velocity-squared of the molecules in a gas. It is given by the formula<ref>
			{{cite book
			\| title = College Physics, Volume 1
			\| edition = 9th
			\| author = Raymond A. Serway, Jerry S. Faughn, and Chris Vuille
			\| publisher = 9780840068484
			\| year = 2011
			\| isbn =
			\| page = 352
			\| url = http://books.google.com/books?id=HLxV-IKYO5IC&pg=PA352
			}}</ref>

			:<math>v_\mathrm{rms} = \sqrt {{3RT}\over{M_m}}</math>

			where ''v''<sub>rms</sub> is the [[root mean square]] of the speed in meters per second, ''M<sub>m</sub>'' is the [[molar mass]] of the gas in kilograms per mole, ''R'' is the [[molar gas constant]], and ''T'' is the [[temperature]] in [[kelvin]]. Although the molecules in a sample of gas have an average kinetic energy (and therefore an average speed) the individual molecules move at various speeds and they stop and change direction according to the law of density measurements and isolation, i.e. they exhibit a distribution of speeds. Some move fast, others relatively slowly. Collisions change individual molecular speeds but the distribution of speeds remains the same. This equation is derived from kinetic theory of gases using [[Maxwell–Boltzmann distribution]] function. The higher the temperature, the greater the mean velocity will be. This works well for both nearly ideal, atomic gases like [[helium]] and for [[Molecule\|molecular gas]]es like diatomic [[oxygen]]. This is because despite the larger internal energy in many molecules (compared to that for an atom), 3''RT''/2 is still the mean [[Translation (physics)\|translational]] [[kinetic energy\|kinetic]] energy.
			This can also be written in terms of the [[Boltzmann constant]] (''k'') as

			:<math>v_\mathrm{rms} = \sqrt {{3kT}\over{m}}</math>

			where ''m'' is the mass of one molecule of the gas.

			This can be derived with energy methods:

			:<math>E_\mathrm{k} = {{3}\over{2}}nRT = \frac{3}{2}NkT</math>
			where ''E''<sub>k</sub> is the [[kinetic energy]] and ''N'' is the number of gas molecules.
			:<math>E_\mathrm{k,molecule} = {{1}\over{2}}mv^2</math>
			Given that ''v''<sup>2</sup> ignores direction, it is logical to assume that the formula can be extended to the entire sample, replacing ''m'' with the entire sample's mass, equal to the molar mass times the number of moles ''n'' yielding
			:<math>{{1}\over{2}}nMv^2 = E_\mathrm{k}</math>
			Therefore
			:<math>v_\mathrm{rms} = \sqrt {{2E_\mathrm{k}}\over{m}}</math>
			which is equivalent.

			The same result is obtained by solving the [[Gaussian integral]] containing the [[Maxwell speed distribution]], ''p''(''v''):
			<!-- The \,\! is to keep the formula rendered as PNG instead of HTML. Please don't remove it.-->
			:<math>v_\mathrm{rms} = \sqrt{\int_{0}^{\infty} v^2\ p(v)dv}\,\! </math>
			::<math> = \sqrt{\int_{0}^{\infty} 4 \pi \left (\frac{m}{2 \pi k T} \right )^\frac{3}{2} v^4\ e^{-\frac{v^{2}m}{2kT}}dv}\,\!</math>
			::<math> = \sqrt{4 \pi \left (\frac{m}{2 \pi k T} \right )^\frac{3}{2} \frac{3}{8} \pi^{\frac{1}{2}} \left( \frac{2kT}{m}\right)^{\frac{5}{2}}}\,\!</math>
			::<math> = \sqrt{\frac{3kT}{m}}</math>

			==References==

			{{reflist}}

			{{DEFAULTSORT:Root Mean Square Speed}}
			[[Category:Gases]]

50.58.204.5: /* Background & Theory */

2012-08-10T18:14:23Z

Background & Theory

New page

Hi there, I am Alyson Pomerleau and I believe it seems fairly great when you say it. Office supervising is what she does for a residing. For a whilst I've been in Alaska but I will have to move in a year or two. The preferred pastime for him and his children is to play lacross and he would never give it up.<br><br>Here is my site; [http://www.acorntown.com/space.php?uid=763416&do=blog&id=738203 love psychic]