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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN">  <HTML> <HEAD> <TITLE>II THE SECOND LAW OF THERMODYNAMICS</TITLE> <META NAME="description" CONTENT="II THE SECOND LAW OF THERMODYNAMICS"> <META NAME="keywords" CONTENT="notes"> <META NAME="resource-type" CONTENT="document"> <META NAME="distribution" CONTENT="global"> <META NAME="Generator" CONTENT="LaTeX2HTML v2002-2-1"> <META HTTP-EQUIV="Content-Style-Type" CONTENT="text/css"> <LINK REL="STYLESHEET" HREF="notes.css"> <LINK REL="next" HREF="node70.html"> <LINK REL="previous" HREF="node8.html"> <LINK REL="up" HREF="notes.html"> <LINK REL="next" HREF="node31.html"> </HEAD> <BODY bgcolor="#ffffff" marginheight=0 marginwidth=0 topmargin=0 leftmargin=0> <table width=100% cellpadding=0 cellspacing=0 border=0 bgcolor="#000000"> <tr> <td colspan=2 width=100% height=50 align=left bgcolor="#003366"> <img src="scaled_composites.jpg" alt="Burt Rutan's White Knight and SpaceShip One, Photo Courtesy of Scaled Composites" border=0> </td> </tr> <tr> <td colspan=2 width=100% height=5 align=right bgcolor="#000000"> <a href="notes.html"> Thermodynamics and Propulsion </a> </td> </tr> <tr> <td width=100% colspan=2 height=20 align=left bgcolor=#cccccc valign=center>   </td> </tr> </table> <table cellpadding=5 cellspacing=0 border=0> <tr> <td bgcolor="#ffffff" valign=top> <DIV CLASS="navigation"> <A NAME="tex2html1215" HREF="node31.html"> <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> <A NAME="tex2html1209" HREF="notes.html"> <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> <A NAME="tex2html1203" HREF="node29.html"> <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A> <A NAME="tex2html1211" HREF="node5.html"> <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A> <A NAME="tex2html1213" HREF="node139.html"> <IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index" SRC="index.png"></A> Next: <A NAME="tex2html1216" HREF="node31.html">4. Background to the</A> Up: <A NAME="tex2html1210" HREF="notes.html">16.Unified: Thermodynamics and Propulsion</A> Previous: <A NAME="tex2html1204" HREF="node29.html">3.8 Muddiest points on</A>   <A NAME="tex2html1212" HREF="node5.html">Contents</A>   <A NAME="tex2html1214" HREF="node139.html">Index</A> </DIV>  <H1><A NAME="SECTION05000000000000000000"></A> <A NAME="prt:SecondLaw"></A> II THE SECOND LAW OF THERMODYNAMICS </H1> <HR>  <A NAME="CHILD_LINKS">Subsections</A> <UL CLASS="ChildLinks"> <LI><A NAME="tex2html1217" HREF="node31.html">4. Background to the Second Law of Thermodynamics</A> <UL> <LI><A NAME="tex2html1218" HREF="node32.html">4.1 Reversibility and Irreversibility in Natural Processes</A> <LI><A NAME="tex2html1219" HREF="node33.html">4.2 Difference between Free and Isothermal Expansions</A> <LI><A NAME="tex2html1220" HREF="node34.html">4.3 Features of reversible processes </A> <LI><A NAME="tex2html1221" HREF="node35.html">4.4 Muddiest Points on Chapter 4</A> </UL> <LI><A NAME="tex2html1222" HREF="node36.html">5. The Second Law of Thermodynamics</A> <UL> <LI><A NAME="tex2html1223" HREF="node37.html">5.1 Concept and Statements of the Second Law</A> <LI><A NAME="tex2html1224" HREF="node38.html">5.2 Axiomatic Statements of the Laws of Thermodynamics</A> <UL> <LI><A NAME="tex2html1225" HREF="node38.html#SECTION05221000000000000000">5.2.1 Introduction</A> <LI><A NAME="tex2html1226" HREF="node38.html#SECTION05222000000000000000">5.2.2 Zeroth Law</A> <LI><A NAME="tex2html1227" HREF="node38.html#SECTION05223000000000000000">5.2.3 First Law</A> <LI><A NAME="tex2html1228" HREF="node38.html#SECTION05224000000000000000">5.2.4 Second Law</A> <LI><A NAME="tex2html1229" HREF="node38.html#SECTION05225000000000000000">5.2.5 Reversible Processes</A> </UL> <LI><A NAME="tex2html1230" HREF="node39.html">5.3 Combined First and Second Law Expressions</A> <LI><A NAME="tex2html1231" HREF="node40.html">5.4 Entropy Changes in an Ideal Gas</A> <LI><A NAME="tex2html1232" HREF="node41.html">5.5 Calculation of Entropy Change in Some Basic Processes</A> <LI><A NAME="tex2html1233" HREF="node42.html">5.6 Muddiest Points on Chapter 5</A> </UL> <LI><A NAME="tex2html1234" HREF="node43.html">6. Applications of the Second Law</A> <UL> <LI><A NAME="tex2html1235" HREF="node44.html">6.1 Limitations on the Work that Can be Supplied by a Heat Engine</A> <LI><A NAME="tex2html1236" HREF="node45.html">6.2 The Thermodynamic Temperature Scale</A> <LI><A NAME="tex2html1237" HREF="node46.html">6.3 Representation of Thermodynamic Processes in  <IMG WIDTH="31" HEIGHT="17" ALIGN="BOTTOM" BORDER="0" SRC="img8.png" ALT="$ T\textrm {-}s$"> coordinates</A> <LI><A NAME="tex2html1238" HREF="node47.html">6.4 Brayton Cycle in <IMG WIDTH="17" HEIGHT="17" ALIGN="BOTTOM" BORDER="0" SRC="img3.png" ALT="$ T$"> -<IMG WIDTH="12" HEIGHT="16" ALIGN="BOTTOM" BORDER="0" SRC="img7.png" ALT="$ s$"> Coordinates</A> <UL> <LI><A NAME="tex2html1239" HREF="node47.html#SECTION05341000000000000000">6.4.1 Net work per unit mass flow in a Brayton cycle</A> </UL> <LI><A NAME="tex2html1240" HREF="node48.html">6.5 Irreversibility, Entropy Changes, and ``Lost Work''</A> <LI><A NAME="tex2html1241" HREF="node49.html">6.6 Entropy and Unavailable Energy</A> <LI><A NAME="tex2html1242" HREF="node50.html">6.7 Examples of Lost Work in Engineering Processes</A> <LI><A NAME="tex2html1243" HREF="node51.html">6.8 Some Overall Comments on Entropy</A> <UL> <LI><A NAME="tex2html1244" HREF="node51.html#SECTION05381000000000000000">6.8.1 Entropy</A> <LI><A NAME="tex2html1245" HREF="node51.html#SECTION05382000000000000000">6.8.2 Reversible and Irreversible Processes</A> <LI><A NAME="tex2html1246" HREF="node51.html#SECTION05383000000000000000">6.8.3 Examples of Reversible and Irreversible Processes</A> </UL> <LI><A NAME="tex2html1247" HREF="node52.html">6.9 Muddiest Points on Chapter 6</A> </UL> <LI><A NAME="tex2html1248" HREF="node53.html">7. Entropy on the Microscopic Scale</A> <UL> <LI><A NAME="tex2html1249" HREF="node54.html">7.1 Entropy Change in Mixing of Two Ideal Gases</A> <LI><A NAME="tex2html1250" HREF="node55.html">7.2 Microscopic and Macroscopic Descriptions of a System </A> <LI><A NAME="tex2html1251" HREF="node56.html">7.3 A Statistical Definition of Entropy </A> <LI><A NAME="tex2html1252" HREF="node57.html">7.4 The Statistical Definition of Entropy and Randomness</A> <LI><A NAME="tex2html1253" HREF="node58.html">7.5 Numerical Example: the Equilibrium Distribution</A> <LI><A NAME="tex2html1254" HREF="node59.html">7.6 Summary and Conclusions</A> </UL> <LI><A NAME="tex2html1255" HREF="node60.html">8. Power Cycles with Two-Phase Media</A> <UL> <LI><A NAME="tex2html1256" HREF="node61.html">8.1 Behavior of Two-Phase Systems</A> <LI><A NAME="tex2html1257" HREF="node62.html">8.2 Work and Heat Transfer with Two-Phase Media</A> <LI><A NAME="tex2html1258" HREF="node63.html">8.3 The Carnot Cycle as a Two-Phase Power Cycle</A> <UL> <LI><A NAME="tex2html1259" HREF="node63.html#SECTION05531000000000000000">8.3.1 Example: Carnot steam cycle</A> </UL> <LI><A NAME="tex2html1260" HREF="node64.html">8.4 The Clausius-Clapeyron Equation</A> <LI><A NAME="tex2html1261" HREF="node65.html">8.5 Rankine Power Cycles</A> <LI><A NAME="tex2html1262" HREF="node66.html">8.6 Enhancements of Rankine Cycles</A> <LI><A NAME="tex2html1263" HREF="node67.html">8.7 Combined Cycles for Power Production</A> <LI><A NAME="tex2html1264" HREF="node68.html">8.8 Some Overall Comments on Thermodynamic Cycles</A> <LI><A NAME="tex2html1265" HREF="node69.html">8.9 Muddiest Points on Chapter 8</A> </UL></UL>  <DIV CLASS="navigation"><HR>  <A NAME="tex2html1215" HREF="node31.html"> <IMG WIDTH="37" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="next" SRC="next.png"></A> <A NAME="tex2html1209" HREF="notes.html"> <IMG WIDTH="26" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="up" SRC="up.png"></A> <A NAME="tex2html1203" HREF="node29.html"> <IMG WIDTH="63" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="previous" SRC="prev.png"></A> <A NAME="tex2html1211" HREF="node5.html"> <IMG WIDTH="65" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="contents" SRC="contents.png"></A> <A NAME="tex2html1213" HREF="node139.html"> <IMG WIDTH="43" HEIGHT="24" ALIGN="BOTTOM" BORDER="0" ALT="index" SRC="index.png"></A> Next: <A NAME="tex2html1216" HREF="node31.html">4. Background to the</A> Up: <A NAME="tex2html1210" HREF="notes.html">16.Unified: Thermodynamics and Propulsion</A> Previous: <A NAME="tex2html1204" HREF="node29.html">3.8 Muddiest points on</A>   <A NAME="tex2html1212" HREF="node5.html">Contents</A>   <A NAME="tex2html1214" HREF="node139.html">Index</A> </DIV>  <ADDRESS> UnifiedTP </ADDRESS> </BODY> </HTML>