Energy balance in an expanding Universe - Revision history

Igor at 16:40, 13 October 2012

2012-10-13T16:40:26Z

Igor at 16:40, 13 October 2012

2012-10-13T16:40:09Z

Igor at 10:12, 10 August 2012

2012-08-10T10:12:31Z

Cosmo All at 16:30, 23 July 2012

2012-07-23T16:30:51Z

Cosmo All at 16:24, 23 July 2012

2012-07-23T16:24:24Z

Cosmo All: Created page with "Category:Dynamics of the Expanding Universe = Energy balance in an expanding Universe =
=== Problem 1. === Show that the first Friedman equation..."

2012-06-18T21:31:37Z

Created page with "Category:Dynamics of the Expanding Universe = Energy balance in an expanding Universe = <div id="equ_en1"></div> === Problem 1. === Show that the first Friedman equation..."

New page

[[Category:Dynamics of the Expanding Universe]]

= Energy balance in an expanding Universe =

<div id="equ_en1"></div>
=== Problem 1. ===
Show that the first Friedman equation can be treated as the energy conservation law in Newtonian mechanics. Use this equation to classify the solutions describing different dynamics of the Universe.
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<div class="NavHead">solution</div>
<div style="width:100%;" class="NavContent">
<p style="text-align: left;">See [[Newtonian_cosmology#equ48|problem]].</p>
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</div>

<div id="equ_en2"></div>
=== Problem 2. ===
Obtain the conservation equation for the expanding Universe using only thermodynamical considerations.
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<div class="NavHead">solution</div>
<div style="width:100%;" class="NavContent">
<p style="text-align: left;">Let $E$ be the total energy inside the volume $V$, and $\rho$ is the energy density in the Universe, then
\[dE = d(\rho V)= Vd\rho+\rho dV.\]
In the first principle of thermodynamics $dQ = dE+pdV$, as the Universe is a closed system by definition, it is evident that $dQ=0$. Taking into account that $dV = 4\pi a^2da$, it is easy to see that
\[\dot{\rho}+3\frac{\dot{a}}{a}(\rho+p)=0.\]</p>
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</div>

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=== Problem 3. ===
A photon's wavelength is redshifted due to the Universe' expansion. Estimate the rate of change of the energy of the Universe due to this process.
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<div class="NavHead">solution</div>
<div style="width:100%;" class="NavContent">
<p style="text-align: left;"></p>
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 [[Category:Dynamics of the Expanding Universe|7]]
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 === Problem 1: Newtonian interpretation ===

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 [[Category:Dynamics of the Expanding Universe|7]]
 __TOC__
-<div id="equ_en1"></div>
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 === Problem 1: Newtonian interpretation ===
 Show that the first Friedman equation can be treated as the energy conservation law in Newtonian mechanics. Use this equation to classify the solutions describing different dynamics of the Universe.
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    <div class="NavHead">solution</div>
    <div style="width:100%;" class="NavContent">
-     <p style="text-align: left;">See [[Newtonian_cosmology#equ48|problem]].</p>
+     <p style="text-align: left;">See [[Newtonian_cosmology#equ48|here]].</p>
    </div>
-</div>
+</div></div>
-<div id="equ_en2"></div>
+<div id="equ_en2"></div><div style="border: 1px solid #AAA; padding:5px;">
 === Problem 2: thermodynamic derivation ===
 Obtain the conservation equation for the expanding Universe using only thermodynamical considerations.
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 \[\dot{\rho}+3\frac{\dot{a}}{a}(\rho+p)=0.\]</p>
    </div>
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+</div></div>
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+<div id="equ_en3"></div><div style="border: 1px solid #AAA; padding:5px;">
 === Problem 3: the lost energy of the Universe ===
 A photon's wavelength is redshifted due to the Universe' expansion. Estimate the rate of change of the energy of the Universe due to this process.
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-   <div class="NavHead">solution</div>
+   <div class="NavHead">no solution</div>
    <div style="width:100%;" class="NavContent">
      <p style="text-align: left;"></p>
    </div>
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← Older revision		Revision as of 16:24, 23 July 2012
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−	[[Category:Dynamics of the Expanding Universe]]	+	[[Category:Dynamics of the Expanding Universe\|7]]

	= Energy balance in an expanding Universe =		= Energy balance in an expanding Universe =

Energy balance in an expanding Universe - Revision history

Igor at 16:40, 13 October 2012

Igor at 16:40, 13 October 2012

Igor at 10:12, 10 August 2012

Cosmo All at 16:30, 23 July 2012

Cosmo All at 16:24, 23 July 2012

Cosmo All: Created page with "Category:Dynamics of the Expanding Universe = Energy balance in an expanding Universe = === Problem 1. === Show that the first Friedman equation..."

Cosmo All: Created page with "Category:Dynamics of the Expanding Universe = Energy balance in an expanding Universe =
=== Problem 1. === Show that the first Friedman equation..."