Template:Arrhenius formulation - Revision history

Richard House: Redirected page to Arrhenius Relationship

2012-08-16T03:38:58Z

Redirected page to Arrhenius Relationship

← Older revision		Revision as of 03:38, 16 August 2012
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	~~===Formulation===~~		#REDIRECT [[Arrhenius_Relationship]]
	~~The Arrhenius reaction rate equation is given by:~~

	~~<br>~~
	~~::<math>R(T)=A{{e}^{-\tfrac{{{E}_{A}}}{K\cdot T}}}</math>~~
	~~<br>~~

	~~where:~~
	~~<br>~~

	~~• <math>R</math> is the speed of reaction.~~
	~~<br>~~
	~~• <math>A</math> is an unknown nonthermal constant.~~
	~~<br>~~
	~~• <math>{{E}_{A}}</math> is the activation energy ( <math>eV</math> ).~~
	~~<br>~~
	~~• <math>K</math> is the Boltzman's constant (<math>8.617385\times {{10}^{-5}}\text{eV}{{\text{K}}^{-1}})</math>~~
	~~<br>~~
	~~• <math>T</math> is the absolute temperature (Kelvin <math>)</math> .~~
	~~<br>~~

	~~The activation energy is the energy that a molecule must have to participate in the reaction. In other words, the activation energy is a measure of the effect that temperature has on the reaction.~~
	~~<br>~~

	~~The Arrhenius life-stress model is formulated by assuming that life is proportional to the inverse reaction rate of the process, thus the Arrhenius life-stress relationship is given by:~~


	~~<br>~~
	~~::<math>L(V)=C{{e}^{\tfrac{B}{V}}}</math>~~

	~~<br>~~
	~~where:~~

	~~• <math>L</math> represents a quantifiable life measure, such as mean life, characteristic life, median life, or <math>B(x)</math> life, etc.~~
	~~<br>~~
	~~• <math>V</math> represents the stress level (formulated for temperature and '''temperature values in absolute units, degrees Kelvin or degrees Rankine''' ).~~
	~~<br>~~
	~~• <math>C</math> is one of the model parameters to be determined, ( <math>C>0).</math>~~
	~~<br>~~
	~~• <math>B</math> is another model parameter to be determined.~~
	~~<br>~~
	~~<br>~~


	[[~~Image:ALTA6.1.png\|center\|400px\|Graphical look at the Arrhenius life-stress relationship (linear scale) for a different life characteristics, assuming a Weibull distribution.~~]]


	Since the Arrhenius is a physics-based model derived for temperature dependence, it is used for temperature accelerated tests. For the same reason, temperature values must be in absolute units (Kelvin or Rankine), even though the Arrhenius equation is unitless.

Chris Kahn: /* Formulation */

2012-06-22T15:28:34Z

Formulation

← Older revision		Revision as of 15:28, 22 June 2012
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	[[Image:ALTA6.1.png\|center\|~~200px~~\|Graphical look at the Arrhenius life-stress relationship (linear scale) for a different life characteristics, assuming a Weibull distribution.]]		[[Image:ALTA6.1.png\|center\|400px\|Graphical look at the Arrhenius life-stress relationship (linear scale) for a different life characteristics, assuming a Weibull distribution.]]


	Since the Arrhenius is a physics-based model derived for temperature dependence, it is used for temperature accelerated tests. For the same reason, temperature values must be in absolute units (Kelvin or Rankine), even though the Arrhenius equation is unitless.		Since the Arrhenius is a physics-based model derived for temperature dependence, it is used for temperature accelerated tests. For the same reason, temperature values must be in absolute units (Kelvin or Rankine), even though the Arrhenius equation is unitless.

Lisa Hacker: /* Formulation */

2012-06-06T17:10:24Z

Formulation

← Older revision		Revision as of 17:10, 6 June 2012
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	• <math>T</math> is the absolute temperature (Kelvin <math>)</math> .		• <math>T</math> is the absolute temperature (Kelvin <math>)</math> .
	<br>		<br>

	The activation energy is the energy that a molecule must have to participate in the reaction. In other words, the activation energy is a measure of the effect that temperature has on the reaction.		The activation energy is the energy that a molecule must have to participate in the reaction. In other words, the activation energy is a measure of the effect that temperature has on the reaction.
	<br>		<br>

Lisa Hacker: /* Formulation */

2012-06-06T17:10:09Z

Formulation

← Older revision		Revision as of 17:10, 6 June 2012
Line 21:		Line 21:
	The activation energy is the energy that a molecule must have to participate in the reaction. In other words, the activation energy is a measure of the effect that temperature has on the reaction.		The activation energy is the energy that a molecule must have to participate in the reaction. In other words, the activation energy is a measure of the effect that temperature has on the reaction.
	<br>		<br>

	The Arrhenius life-stress model is formulated by assuming that life is proportional to the inverse reaction rate of the process, thus the Arrhenius life-stress relationship is given by:		The Arrhenius life-stress model is formulated by assuming that life is proportional to the inverse reaction rate of the process, thus the Arrhenius life-stress relationship is given by:

Chuck Smith: /* Formulation */

2012-04-26T15:58:25Z

Formulation

← Older revision		Revision as of 15:58, 26 April 2012
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	[[Image:ALTA6.1.png\|center\|~~400px~~\|Graphical look at the Arrhenius life-stress relationship (linear scale) for a different life characteristics, assuming a Weibull distribution.]]		[[Image:ALTA6.1.png\|center\|200px\|Graphical look at the Arrhenius life-stress relationship (linear scale) for a different life characteristics, assuming a Weibull distribution.]]


	Since the Arrhenius is a physics-based model derived for temperature dependence, it is used for temperature accelerated tests. For the same reason, temperature values must be in absolute units (Kelvin or Rankine), even though the Arrhenius equation is unitless.		Since the Arrhenius is a physics-based model derived for temperature dependence, it is used for temperature accelerated tests. For the same reason, temperature values must be in absolute units (Kelvin or Rankine), even though the Arrhenius equation is unitless.

Nicolette Young: /* Formulation */

2012-03-23T17:48:55Z

Formulation

← Older revision		Revision as of 17:48, 23 March 2012
Line 41:		Line 41:


	[[Image:ALTA6.1.~~jpg~~\|center\|400px\|Graphical look at the Arrhenius life-stress relationship (linear scale) for a different life characteristics, assuming a Weibull distribution.]]		[[Image:ALTA6.1.png\|center\|400px\|Graphical look at the Arrhenius life-stress relationship (linear scale) for a different life characteristics, assuming a Weibull distribution.]]


	Since the Arrhenius is a physics-based model derived for temperature dependence, it is used for temperature accelerated tests. For the same reason, temperature values must be in absolute units (Kelvin or Rankine), even though the Arrhenius equation is unitless.		Since the Arrhenius is a physics-based model derived for temperature dependence, it is used for temperature accelerated tests. For the same reason, temperature values must be in absolute units (Kelvin or Rankine), even though the Arrhenius equation is unitless.

Nicolette Young: /* Formulation */

2012-03-23T16:35:51Z

Formulation

← Older revision		Revision as of 16:35, 23 March 2012
Line 41:		Line 41:


	[[Image:ALTA6.1.~~png~~\|center\|400px\|Graphical look at the Arrhenius life-stress relationship (linear scale) for a different life characteristics, assuming a Weibull distribution.]]		[[Image:ALTA6.1.jpg\|center\|400px\|Graphical look at the Arrhenius life-stress relationship (linear scale) for a different life characteristics, assuming a Weibull distribution.]]


	Since the Arrhenius is a physics-based model derived for temperature dependence, it is used for temperature accelerated tests. For the same reason, temperature values must be in absolute units (Kelvin or Rankine), even though the Arrhenius equation is unitless.		Since the Arrhenius is a physics-based model derived for temperature dependence, it is used for temperature accelerated tests. For the same reason, temperature values must be in absolute units (Kelvin or Rankine), even though the Arrhenius equation is unitless.

Nicolette Young: /* Formulation */

2012-03-23T16:26:52Z

Formulation

← Older revision		Revision as of 16:26, 23 March 2012
Line 41:		Line 41:


	[[Image:ALTA6.1.~~gif\|thumb~~\|center\|~~300px~~\|Graphical look at the Arrhenius life-stress relationship (linear scale) for a different life characteristics, assuming a Weibull distribution.]]		[[Image:ALTA6.1.png\|center\|400px\|Graphical look at the Arrhenius life-stress relationship (linear scale) for a different life characteristics, assuming a Weibull distribution.]]


	Since the Arrhenius is a physics-based model derived for temperature dependence, it is used for temperature accelerated tests. For the same reason, temperature values must be in absolute units (Kelvin or Rankine), even though the Arrhenius equation is unitless.		Since the Arrhenius is a physics-based model derived for temperature dependence, it is used for temperature accelerated tests. For the same reason, temperature values must be in absolute units (Kelvin or Rankine), even though the Arrhenius equation is unitless.

Athanasios Gerokostopoulos: /* Formulation */

2012-02-27T23:33:51Z

Formulation

← Older revision		Revision as of 23:33, 27 February 2012
Line 1:		Line 1:
	===Formulation===		===Formulation===
	The Arrhenius reaction rate equation is given by:		The Arrhenius reaction rate equation is given by:

	<br>		<br>
	::<math>R(T)=A{{e}^{-\tfrac{{{E}_{A}}}{K\cdot T}}}</math>		::<math>R(T)=A{{e}^{-\tfrac{{{E}_{A}}}{K\cdot T}}}</math>

Athanasios Gerokostopoulos: /* Formulation */

2012-02-13T23:56:01Z

Formulation

← Older revision		Revision as of 23:56, 13 February 2012
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	==Formulation==		===Formulation===
	The Arrhenius reaction rate equation is given by:		The Arrhenius reaction rate equation is given by:
	<br>		<br>