Entropy of Expanding Universe - Revision history

Cosmo All at 23:29, 8 January 2013

2013-01-08T23:29:41Z

2012-10-01T22:17:32Z

‎Problem 7

2012-10-01T22:17:04Z

2012-10-01T22:15:42Z

2012-10-01T21:17:58Z

2012-10-01T21:15:02Z

2012-09-30T17:19:32Z

2012-09-30T17:17:32Z

Created page with "(3)"

New page

[[Category:Thermodynamics of Universe|(3)]]

@@ Line 192: / Line 192: @@
 \frac{1}{T}\frac{dT}{dt} =  - \frac{1}{3V}\frac{dV}{dt},\] or equivalently \[ \frac{d}{dt}(\ln T) =  - \frac{d}{dt}(\ln a)\Rightarrow aT = const.
 \]</p>
    </div>
 </div></div>

@@ Line 104: / Line 104: @@
    <div class="NavHead">solution</div>
    <div style="width:100%;" class="NavContent">
-     <p style="text-align: left;">Size of the observable part of the Universe is $l_{H0}  \sim 10^{28} \mbox{\it cm}$ and therefore
+     <p style="text-align: left;">Size of the observable part of the Universe is $l_{H0}  \sim 10^{28} \mbox{cm}$ and therefore
 \[S = \frac{4\pi}{3}sl_{H0}^3  \sim 10^{88}.\]</p>
    </div>
@@ Line 113: / Line 113: @@
 <div id="ter_10"></div>
 <div style="border: 1px solid #AAA; padding:5px;">
 === Problem 7 ===
 Why is the expansion of the Universe described by the Friedman equations adiabatic?

@@ Line 11: / Line 11: @@
    <div class="NavHead">solution</div>
    <div style="width:100%;" class="NavContent">
-     <p style="text-align: left;">
+     <p style="text-align: left;"></p>
 <div id="therm29"></div>

@@ Line 22: / Line 22: @@
 <div style="border: 1px solid #AAA; padding:5px;">
 === Problem 2 ===
- Find the entropy density for the photon gas.
+Find the entropy density for the photon gas.
 <div class="NavFrame collapsed">
    <div class="NavHead">solution</div>
    <div style="width:100%;" class="NavContent">
      <p style="text-align: left;">
 \[
-   dS = \frac{dE}
+   dS = \frac{dE}{T} + \frac{pdV}{T} = \frac{V}{T}\frac{d\rho}{dT}dT + \frac{\rho+ p}{T}dV \Rightarrow\] \[  \left( \frac{\partial S}{\partial V}
 {T} + \frac{pdV} {T} = \frac{V}{T}\frac{d\rho}{dT}dT + \frac{\rho+ p} {T}dV \Rightarrow\] \[  \left( \frac{\partial S}{\partial V}
 \right)_T = \frac{\rho + p} {T} \Rightarrow
    S = \frac{\rho  + p}{T}V + f(T).\]
@@ Line 45: / Line 43: @@
 </div></div>
 <div id="therm30"></div>
@@ Line 126: / Line 111: @@
 <div style="border: 1px solid #AAA; padding:5px;">
 === Problem 7 ===
- Estimate the entropy of the observable part of the Universe.
+Estimate the entropy of the observable part of the Universe.
 <div class="NavFrame collapsed">
    <div class="NavHead">solution</div>

← Older revision		Revision as of 17:19, 30 September 2012
Line 1:		Line 1:
−	[[Category:Thermodynamics of Universe\|(3)]]	+	[[Category:Thermodynamics of Universe\|3]]