Thermodynamics of Non-Relativistic Gas - Revision history

Cosmo All: /* Problem 3 */

2012-11-01T10:08:26Z

‎Problem 3

Den at 20:32, 1 October 2012

2012-10-01T20:32:13Z

Den at 20:30, 1 October 2012

2012-10-01T20:30:14Z

Den at 20:29, 1 October 2012

2012-10-01T20:29:07Z

Den at 20:23, 1 October 2012

2012-10-01T20:23:01Z

Show changes

Den at 18:35, 1 October 2012

2012-10-01T18:35:45Z

Cosmo All at 17:19, 30 September 2012

2012-09-30T17:19:26Z

Cosmo All: Created page with "(2)"

2012-09-30T17:17:26Z

Created page with "(2)"

New page

[[Category:Thermodynamics of Universe|(2)]]

@@ Line 42: / Line 42: @@
 <div style="border: 1px solid #AAA; padding:5px;">
 === Problem 3 ===
-ow that in the non-relativistic limit ($kT\ll mc^2$) $p\ll\rho$.
+Show that in the non-relativistic limit ($kT\ll mc^2$) $p\ll\rho$.
 <div class="NavFrame collapsed">
    <div class="NavHead">solution</div>
@@ Line 59: / Line 59: @@
 <div id="ter_n_19"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
 === Problem 4 ===
 Show that for a system of particles in thermal equilibrium the following holds

← Older revision		Revision as of 20:32, 1 October 2012
Line 2:		Line 2:


−	~~__TOC__~~	+	__NOTOC__

@@ Line 100: / Line 100: @@
 <div style="border: 1px solid #AAA; padding:5px;">
 === Problem 6 ===
- Show that for a substance with the equation of state $p=w\rho$ the following holds $T\propto a^{-3w}.$
+Show that for a substance with the equation of state $p=w\rho$ the following holds $T\propto a^{-3w}.$
 <div class="NavFrame collapsed">
    <div class="NavHead">solution</div>

@@ Line 100: / Line 100: @@
 <div style="border: 1px solid #AAA; padding:5px;">
 === Problem 6 ===
-  Show that for a substance with the equation of state $p=w\rho$ the following holds
+  Show that for a substance with the equation of state $p=w\rho$ the following holds $T\propto a^{-3w}.$
-\[T\propto a^{-3w}.\]
 <div class="NavFrame collapsed">
    <div class="NavHead">solution</div>
    <div style="width:100%;" class="NavContent">
      <p style="text-align: left;">
 \[T\propto\rho^{\frac{w}{w+1}},\ \rho\propto a^{-3(1+w)}\Rightarrow T\propto a^{-3w}.\]
   </p>
@@ Line 116: / Line 114: @@
 <div style="border: 1px solid #AAA; padding:5px;">
 === Problem 7 ===
-Obtain a generalization of Stefan-Boltzmann law for cosmological fluid, described by generalized polytropic equation of state \[p=w\rho+k\rho^{1+1/n},\]
+Obtain a generalization of Stefan-Boltzmann law for cosmological fluid, described by generalized polytropic equation of state $p=w\rho+k\rho^{1+1/n},$ assuming that $1+w+k\rho^{1/n}>0$.
-    assuming that $1+w+k\rho^{1/n}>0$.
 <div class="NavFrame collapsed">
    <div class="NavHead">solution</div>

← Older revision		Revision as of 18:35, 1 October 2012
Line 1:		Line 1:
	[[Category:Thermodynamics of Universe\|2]]		[[Category:Thermodynamics of Universe\|2]]
		+
		+
		+	__TOC__
		+
		+
		+	<div id="ter_9"></div>
		+	<div style="border: 1px solid #AAA; padding:5px;">
		+	=== Problem 11 ===
		+
		+	<div class="NavFrame collapsed">
		+	<div class="NavHead">solution</div>
		+	<div style="width:100%;" class="NavContent">
		+	<p style="text-align: left;">
		+
		+
		+	</p>
		+	</div>
		+	</div></div>
		+
		+
		+	<div id="ter_9"></div>
		+	<div style="border: 1px solid #AAA; padding:5px;">
		+	=== Problem 11 ===
		+
		+	<div class="NavFrame collapsed">
		+	<div class="NavHead">solution</div>
		+	<div style="width:100%;" class="NavContent">
		+	<p style="text-align: left;">
		+
		+
		+	</p>
		+	</div>
		+	</div></div>
		+
		+
		+	<div id="ter_9"></div>
		+	<div style="border: 1px solid #AAA; padding:5px;">
		+	=== Problem 11 ===
		+
		+	<div class="NavFrame collapsed">
		+	<div class="NavHead">solution</div>
		+	<div style="width:100%;" class="NavContent">
		+	<p style="text-align: left;">
		+
		+
		+	</p>
		+	</div>
		+	</div></div>
		+
		+
		+	<div id="ter_9"></div>
		+	<div style="border: 1px solid #AAA; padding:5px;">
		+	=== Problem 11 ===
		+
		+	<div class="NavFrame collapsed">
		+	<div class="NavHead">solution</div>
		+	<div style="width:100%;" class="NavContent">
		+	<p style="text-align: left;">
		+
		+
		+	</p>
		+	</div>
		+	</div></div>
		+
		+
		+	<div id="ter_9"></div>
		+	<div style="border: 1px solid #AAA; padding:5px;">
		+	=== Problem 11 ===
		+
		+	<div class="NavFrame collapsed">
		+	<div class="NavHead">solution</div>
		+	<div style="width:100%;" class="NavContent">
		+	<p style="text-align: left;">
		+
		+
		+	</p>
		+	</div>
		+	</div></div>
		+
		+
		+	<div id="ter_9"></div>
		+	<div style="border: 1px solid #AAA; padding:5px;">
		+	=== Problem 11 ===
		+
		+	<div class="NavFrame collapsed">
		+	<div class="NavHead">solution</div>
		+	<div style="width:100%;" class="NavContent">
		+	<p style="text-align: left;">
		+
		+
		+	</p>
		+	</div>
		+	</div></div>
		+
		+
		+	<div id="ter_9"></div>
		+	<div style="border: 1px solid #AAA; padding:5px;">
		+	=== Problem 11 ===
		+
		+	<div class="NavFrame collapsed">
		+	<div class="NavHead">solution</div>
		+	<div style="width:100%;" class="NavContent">
		+	<p style="text-align: left;">
		+
		+
		+	</p>
		+	</div>
		+	</div></div>
		+
		+
		+	<div id="ter_9"></div>
		+	<div style="border: 1px solid #AAA; padding:5px;">
		+	=== Problem 11 ===
		+
		+	<div class="NavFrame collapsed">
		+	<div class="NavHead">solution</div>
		+	<div style="width:100%;" class="NavContent">
		+	<p style="text-align: left;">
		+
		+
		+	</p>
		+	</div>
		+	</div></div>

← Older revision		Revision as of 17:19, 30 September 2012
Line 1:		Line 1:
−	[[Category:Thermodynamics of Universe\|(2)]]	+	[[Category:Thermodynamics of Universe\|2]]