Difference between revisions of "User:Tohline/PGE/FirstLawOfThermodynamics"
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Following the detailed discussion of the laws of thermodynamics that can be found, for example in Chapter I of [<b>[[User:Tohline/Appendix/References#C67|<font color="red">C67</font>]]</b>] we know that, "<font color="#007700">for an infinitesimal quasi-statical change of state,</font>" the change <math>~dQ</math> in the total heat content <math>~Q</math> of a fluid element is given by, what we will label as | Following the detailed discussion of the laws of thermodynamics that can be found, for example in Chapter I of [<b>[[User:Tohline/Appendix/References#C67|<font color="red">C67</font>]]</b>] we know that, "<font color="#007700">for an infinitesimal quasi-statical change of state,</font>" the change <math>~dQ</math> in the total heat content <math>~Q</math> of a fluid element is given by, what we will label as, | ||
<div align="center"> | <div align="center"> | ||
<span id=" | <span id="FormA"><font color="#770000">'''Form A'''</font></span><br /> | ||
of the First Law of Thermodyamics | of the First Law of Thermodyamics | ||
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[<b>[[User:Tohline/Appendix/References#C67|<font color="red">C67</font>]]</b>], Chapter II, Eq. (2) | [<b>[[User:Tohline/Appendix/References#C67|<font color="red">C67</font>]]</b>], Chapter II, Eq. (2) | ||
</div> | </div> | ||
where, {{ User:Tohline/Math/VAR_SpecificInternalEnergy01 }} is the specific internal energy, {{ User:Tohline/Math/VAR_Pressure01 }} is the pressure, and {{ User:Tohline/Math/VAR_SpecificVolume01 }}<math>~= 1/</math>{{ User:Tohline/Math/VAR_Density01 }} is the specific volume of the fluid element. | where, {{ User:Tohline/Math/VAR_SpecificInternalEnergy01 }} is the specific internal energy, {{ User:Tohline/Math/VAR_Pressure01 }} is the pressure, and {{ User:Tohline/Math/VAR_SpecificVolume01 }}<math>~= 1/</math>{{ User:Tohline/Math/VAR_Density01 }} is the specific volume of the fluid element. Generally, the change in the total heat content can be rewritten in terms of the gas temperature, {{ User:Tohline/Math/VAR_Temperature01 }}, and the specific entropy of the fluid, {{ User:Tohline/Math/VAR_SpecificEntropy01 }}, via the expression, | ||
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<table border="0" cellpadding="5" align="center"> | |||
<tr> | |||
<td align="right"> | |||
<math>~dQ</math> | |||
</td> | |||
<td align="center"> | |||
<math>~=</math> | |||
</td> | |||
<td align="left"> | |||
<math>~T ds \, .</math> | |||
</td> | |||
</tr> | |||
</table> | |||
[<b>[[User:Tohline/Appendix/References#C67|<font color="red">C67</font>]]</b>], Chapter II, Eq. (44) | |||
</div> | |||
If, in addition, it is understood that the specified changes are occurring over a certain interval of time <math>~dt</math>, then from this pair of expressions we derive what will henceforth be referred to as the, | |||
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<span id="Standard Form"><font color="#770000">'''Standard Form'''</font></span><br /> | |||
of the First Law of Thermodyamics | |||
{{ User:Tohline/Math/EQ_FirstLaw01 }} | |||
[<b>[[User:Tohline/Appendix/References#C67|<font color="red">C67</font>]]</b>], Chapter II, Eq. (2) | |||
</div> | |||
<br /> | <br /> | ||
{{LSU_HBook_footer}} | {{LSU_HBook_footer}} | ||
Revision as of 21:16, 23 October 2018
First Law of Thermodynamics
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Following the detailed discussion of the laws of thermodynamics that can be found, for example in Chapter I of [C67] we know that, "for an infinitesimal quasi-statical change of state," the change <math>~dQ</math> in the total heat content <math>~Q</math> of a fluid element is given by, what we will label as,
Form A
of the First Law of Thermodyamics
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<math>~dQ</math> |
<math>~=</math> |
<math>~ d\epsilon + PdV \, , </math> |
[C67], Chapter II, Eq. (2)
where, <math>~\epsilon</math> is the specific internal energy, <math>~P</math> is the pressure, and <math>~V</math><math>~= 1/</math><math>~\rho</math> is the specific volume of the fluid element. Generally, the change in the total heat content can be rewritten in terms of the gas temperature, <math>~T</math>, and the specific entropy of the fluid, <math>~s</math>, via the expression,
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<math>~dQ</math> |
<math>~=</math> |
<math>~T ds \, .</math> |
[C67], Chapter II, Eq. (44)
If, in addition, it is understood that the specified changes are occurring over a certain interval of time <math>~dt</math>, then from this pair of expressions we derive what will henceforth be referred to as the,
Standard Form
of the First Law of Thermodyamics
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<math>T \frac{ds}{dt} = \frac{d\epsilon}{dt} + P \frac{d}{dt} \biggl(\frac{1}{\rho}\biggr)</math> |
[C67], Chapter II, Eq. (2)
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