User:Tohline/SR/IdealGas - Revision history

Tohline: /* Consequential Ideal Gas Relations */

2019-03-09T22:40:38Z

Consequential Ideal Gas Relations

← Older revision		Revision as of 22:40, 9 March 2019
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	where we have — as have many before us — introduced a key physical parameter,		<span id="gamma_g">where we have — as have many before us — introduced a key physical parameter,</span>
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Tohline: /* Specific Heats */

2018-10-26T21:44:48Z

Specific Heats

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	[<b>[[User:Tohline/Appendix/References#C67\|<font color="red">C67</font>]]</b>], Chapter II, §1, Eq. (9)<br />		[<b>[[User:Tohline/Appendix/References#C67\|<font color="red">C67</font>]]</b>], Chapter II, §1, Eq. (9)<br />
			[http://adsabs.harvard.edu/abs/1968psen.book.....C D. D. Clayton (1968)], Eq. (2-108)<br />
	[<b>[[User:Tohline/Appendix/References#LL75\|<font color="red">LL75</font>]]</b>], Chapter IX, §80, immediately following Eq. (80.11)<br />		[<b>[[User:Tohline/Appendix/References#LL75\|<font color="red">LL75</font>]]</b>], Chapter IX, §80, immediately following Eq. (80.11)<br />
	[<b>[[User:Tohline/Appendix/References#H87\|<font color="red">H87</font>]]</b>], §1.2, p. 9<br>		[<b>[[User:Tohline/Appendix/References#H87\|<font color="red">H87</font>]]</b>], §1.2, p. 9<br>

Tohline: /* Property #1 */

2018-10-26T21:39:36Z

Property #1

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	[<b>[[User:Tohline/Appendix/References#C67\|<font color="red">C67</font>]]</b>], Chapter VII.3, Eq. (18)<br />		[<b>[[User:Tohline/Appendix/References#C67\|<font color="red">C67</font>]]</b>], Chapter VII.3, Eq. (18)<br />
			[http://adsabs.harvard.edu/abs/1968psen.book.....C D. D. Clayton (1968)], Eq. (2-7)<br />
	[<b>[[User:Tohline/Appendix/References#CH87\|<font color="red">H87</font>]]</b>], §1.1, p. 5		[<b>[[User:Tohline/Appendix/References#CH87\|<font color="red">H87</font>]]</b>], §1.1, p. 5
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Tohline: /* Consequential Ideal Gas Relations */

2018-10-26T21:34:14Z

Consequential Ideal Gas Relations

← Older revision		Revision as of 21:34, 26 October 2018
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	where {{User:Tohline/Math/C_GasConstant}} &equiv; {{ User:Tohline/Math/~~C_AvogadroConstant~~ }}{{ User:Tohline/Math/~~C_BoltzmannConstant~~ }} is the gas constant. The definition of the gas constant can be found in the [[User:Tohline/Appendix/Variables_templates\|Variables Appendix]] of this H_Book; its numerical value can be obtained by simply scrolling the computer mouse over its symbol in the text of this paragraph. See §VII.3 (p. 254) of [[User:Tohline/Appendix/References#C67\|[<b><font color="red">C67</font></b>]]] or §13.1 (p. 102) of [[User:Tohline/Appendix/References#KW94\|[<b><font color="red">KW94</font></b>]]] for particularly clear explanations of how to calculate {{User:Tohline/Math/MP_MeanMolecularWeight}}.		where {{User:Tohline/Math/C_GasConstant}} &equiv; {{ User:Tohline/Math/C_BoltzmannConstant }}{{ User:Tohline/Math/C_AvogadroConstant }} is generally referred to in the astrophysics literature as the gas constant. The definition of the gas constant can be found in the [[User:Tohline/Appendix/Variables_templates\|Variables Appendix]] of this H_Book; its numerical value can be obtained by simply scrolling the computer mouse over its symbol in the text of this paragraph. See §VII.3 (p. 254) of [[User:Tohline/Appendix/References#C67\|[<b><font color="red">C67</font></b>]]] or §13.1 (p. 102) of [[User:Tohline/Appendix/References#KW94\|[<b><font color="red">KW94</font></b>]]] for particularly clear explanations of how to calculate {{User:Tohline/Math/MP_MeanMolecularWeight}}.

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	where we — as have many before us — ~~have~~ introduced a key physical parameter,		where we have — as have many before us — introduced a key physical parameter,
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Tohline: /* Ideal Gas Equation of State */

2018-10-26T21:28:54Z

Ideal Gas Equation of State

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	<font color="#007700">where {{ User:Tohline/Math/C_AvogadroConstant }} = 1/{{ User:Tohline/Math/C_AtomicMassUnit }} is Avogadro's number …</font>"		<font color="#007700">where {{ User:Tohline/Math/C_AvogadroConstant }} = 1/{{ User:Tohline/Math/C_AtomicMassUnit }} is Avogadro's number …</font>" Substitution into the [[#Fundamental_Properties_of_an_Ideal_Gas\|above-defined ''Standard Form of the Ideal Gas Equation of State'']] gives, what we will refer to as,

	~~Hence, in place of~~ the above ~~"standard form"~~ of the ~~ideal gas equation~~ of ~~state~~, we ~~more commonly will adopt the following expression, which~~ will ~~be referred~~ to as

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	where {{User:Tohline/Math/C_GasConstant}} ~~is the gas constant and {{User:Tohline/Math/MP_MeanMolecularWeight}} <math>\~~equiv~~</math> {{User:Tohline/Math/VAR_Density01}}/(~~{{User:Tohline/Math/~~C_AtomicMassUnit~~}}{{User:Tohline/Math/~~VAR_NumberDensity01~~}}) is ~~the mean molecular weight of~~ the gas. The definition of the gas constant can be found in the [[User:Tohline/Appendix/Variables_templates\|Variables Appendix]] of this H_Book; its numerical value can be obtained by simply scrolling the computer mouse over its symbol in the text of this paragraph. See §VII.3 (p. 254) of [[User:Tohline/Appendix/References#C67\|[<b><font color="red">C67</font></b>]]] or §13.1 (p. 102) of [[User:Tohline/Appendix/References#KW94\|[<b><font color="red">KW94</font></b>]]] for particularly clear explanations of how to calculate {{User:Tohline/Math/MP_MeanMolecularWeight}}.		where {{User:Tohline/Math/C_GasConstant}} &equiv; {{ User:Tohline/Math/C_AvogadroConstant }}{{ User:Tohline/Math/C_BoltzmannConstant }} is the gas constant. The definition of the gas constant can be found in the [[User:Tohline/Appendix/Variables_templates\|Variables Appendix]] of this H_Book; its numerical value can be obtained by simply scrolling the computer mouse over its symbol in the text of this paragraph. See §VII.3 (p. 254) of [[User:Tohline/Appendix/References#C67\|[<b><font color="red">C67</font></b>]]] or §13.1 (p. 102) of [[User:Tohline/Appendix/References#KW94\|[<b><font color="red">KW94</font></b>]]] for particularly clear explanations of how to calculate {{User:Tohline/Math/MP_MeanMolecularWeight}}.

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	~~Drawing~~ a couple of the expressions from the above discussion of specific heats, the right-hand side of ''Form A of the Ideal Gas Equation of State'' can be rewritten as,		Employing a couple of the expressions from the above discussion of specific heats, the right-hand side of ''Form A of the Ideal Gas Equation of State'' can be rewritten as,
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Tohline: /* Consequential Ideal Gas Relations */

2018-10-26T21:15:43Z

Consequential Ideal Gas Relations

← Older revision		Revision as of 21:15, 26 October 2018
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	==Consequential Ideal Gas Relations==		==Consequential Ideal Gas Relations==

	Throughout most of this H_Book, we will define the relative degree of compression of a gas in terms of its mass density {{User:Tohline/Math/VAR_Density01}} rather than in terms of its number density {{User:Tohline/Math/VAR_NumberDensity01}}. Hence, in place of the above "standard form" of the ideal gas equation of state, we more commonly will adopt the following expression, which will be referred to as		Throughout most of this H_Book, we will define the relative degree of compression of a gas in terms of its mass density {{User:Tohline/Math/VAR_Density01}} rather than in terms of its number density {{User:Tohline/Math/VAR_NumberDensity01}}. Following [http://adsabs.harvard.edu/abs/1968psen.book.....C D. D. Clayton (1968)] — see his p. 82 discussion of ''The Perfect Monatomic Nondegenerate Gas'' — we will "<font color="#007700">let the mean molecular weight of the perfect gas be designated by {{ User:Tohline/Math/MP_MeanMolecularWeight }}. Then the density is</font>

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			<math>~\rho = n_g \bar\mu m_u \, ,</math>
			</div>

			<font color="#007700">where {{ User:Tohline/Math/C_AtomicMassUnit }} is the mass of 1 amu</font>" ([https://en.wikipedia.org/wiki/Unified_atomic_mass_unit atomic mass unit]). "<font color="#007700">The number of particles per unit volume can then be expressed in terms of the density and the mean molecular weight as</font>

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			<math>~n_g = \frac{\rho}{\bar\mu m_u} = \frac{\rho N_A}{\bar\mu} \, ,</math>
			</div>

			<font color="#007700">where {{ User:Tohline/Math/C_AvogadroConstant }} = 1/{{ User:Tohline/Math/C_AtomicMassUnit }} is Avogadro's number …</font>"

			Hence, in place of the above "standard form" of the ideal gas equation of state, we more commonly will adopt the following expression, which will be referred to as

	<div align="center">		<div align="center">

Tohline: /* Consequential Ideal Gas Relations */

2018-10-25T22:44:53Z

Consequential Ideal Gas Relations

← Older revision		Revision as of 22:44, 25 October 2018
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	[<b>[[User:Tohline/Appendix/References#C67\|<font color="red">C67</font>]]</b>], Chapter II, Eq. (5)<br />		[<b>[[User:Tohline/Appendix/References#C67\|<font color="red">C67</font>]]</b>], Chapter II, Eq. (5)<br />
	[<b>[[User:Tohline/Appendix/References#HK94\|<font color="red">HK94</font>]]</b>], §1.3.1, Eq. (1.22)		[<b>[[User:Tohline/Appendix/References#HK94\|<font color="red">HK94</font>]]</b>], §1.3.1, Eq. (1.22)<br />
			[<b>[[User:Tohline/Appendix/References#BLRY07\|<font color="red">BLRY07</font>]]</b>], §6.1.1, Eq. (6.4)
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Tohline: /* Consequential Ideal Gas Relations */

2018-10-25T22:41:43Z

Consequential Ideal Gas Relations

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	{{User:Tohline/Math/EQ_EOSideal02}}		{{User:Tohline/Math/EQ_EOSideal02}}

	[<b>[[User:Tohline/Appendix/References#C67\|<font color="red">C67</font>]]</b>], Chapter II, Eq. (5)		[<b>[[User:Tohline/Appendix/References#C67\|<font color="red">C67</font>]]</b>], Chapter II, Eq. (5)<br />
			[<b>[[User:Tohline/Appendix/References#HK94\|<font color="red">HK94</font>]]</b>], §1.3.1, Eq. (1.22)
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Tohline: /* Consequential Ideal Gas Relations */

2018-10-25T22:29:25Z

Consequential Ideal Gas Relations

← Older revision		Revision as of 22:29, 25 October 2018
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	where we — as have many before us — have introduced a ~~physically important~~ parameter,		where we — as have many before us — have introduced a key physical parameter,
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	[<b>[[User:Tohline/Appendix/References#C67\|<font color="red">C67</font>]]</b>], Chapter II, immediately following Eq. (9)<br />		[<b>[[User:Tohline/Appendix/References#C67\|<font color="red">C67</font>]]</b>], Chapter II, immediately following Eq. (9)<br />
	[<b>[[User:Tohline/Appendix/References#LL75\|<font color="red">LL75</font>]]</b>], Chapter IX, §80, immediately following Eq. (80.9)<br />		[<b>[[User:Tohline/Appendix/References#LL75\|<font color="red">LL75</font>]]</b>], Chapter IX, §80, immediately following Eq. (80.9)<br />
	[<b>[[User:Tohline/Appendix/References#T78\|<font color="red">T78</font>]]</b>], §3.4, immediately following Eq. (72)		[<b>[[User:Tohline/Appendix/References#T78\|<font color="red">T78</font>]]</b>], §3.4, immediately following Eq. (72)<br />
			[<b>[[User:Tohline/Appendix/References#HK94\|<font color="red">HK94</font>]]</b>], §3.7.1, Eq. (3.86)
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Tohline: /* Specific Heats */

2018-10-25T22:27:46Z

Specific Heats

← Older revision		Revision as of 22:27, 25 October 2018
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	[<b>[[User:Tohline/Appendix/References#C67\|<font color="red">C67</font>]]</b>], Chapter II, Eq. (10)<br />		[<b>[[User:Tohline/Appendix/References#C67\|<font color="red">C67</font>]]</b>], Chapter II, Eq. (10)<br />
	[<b>[[User:Tohline/Appendix/References#LL75\|<font color="red">LL75</font>]]</b>], Chapter IX, §80, Eq. (80.10)<br />		[<b>[[User:Tohline/Appendix/References#LL75\|<font color="red">LL75</font>]]</b>], Chapter IX, §80, Eq. (80.10)<br />
	[<b>[[User:Tohline/Appendix/References#H87\|<font color="red">H87</font>]]</b>], §1.2, p. 9		[<b>[[User:Tohline/Appendix/References#H87\|<font color="red">H87</font>]]</b>], §1.2, p. 9<br />
			[<b>[[User:Tohline/Appendix/References#HK94\|<font color="red">HK94</font>]]</b>], §3.7.1, immediately following Eq. (3.80)
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	[<b>[[User:Tohline/Appendix/References#KW94\|<font color="red">KW94</font>]]</b>], §4.1, immediately following Eq. (4.15)		[<b>[[User:Tohline/Appendix/References#KW94\|<font color="red">KW94</font>]]</b>], §4.1, immediately following Eq. (4.15)
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	==Consequential Ideal Gas Relations==		==Consequential Ideal Gas Relations==

← Older revision		Revision as of 21:44, 26 October 2018
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	[<b>[[User:Tohline/Appendix/References#C67\|<font color="red">C67</font>]]</b>], Chapter II, §1, Eq. (9)<br />		[<b>[[User:Tohline/Appendix/References#C67\|<font color="red">C67</font>]]</b>], Chapter II, §1, Eq. (9)<br />
			[http://adsabs.harvard.edu/abs/1968psen.book.....C D. D. Clayton (1968)], Eq. (2-108)<br />
	[<b>[[User:Tohline/Appendix/References#LL75\|<font color="red">LL75</font>]]</b>], Chapter IX, §80, immediately following Eq. (80.11)<br />		[<b>[[User:Tohline/Appendix/References#LL75\|<font color="red">LL75</font>]]</b>], Chapter IX, §80, immediately following Eq. (80.11)<br />
	[<b>[[User:Tohline/Appendix/References#H87\|<font color="red">H87</font>]]</b>], §1.2, p. 9<br>		[<b>[[User:Tohline/Appendix/References#H87\|<font color="red">H87</font>]]</b>], §1.2, p. 9<br>