Difference between revisions of "Thermo warm-up"

From Universe in Problems
Jump to: navigation, search
(Problem 8: Earth and entropy production)
(Problem 9: Sun and entropy production)
 
Line 153: Line 153:
 
<div style="border: 1px solid #AAA; padding:5px;">
 
<div style="border: 1px solid #AAA; padding:5px;">
  
=== Problem 9: Sun and entropy production ===
+
=== Problem 9: Sun's entropy production ===
Show that the Sun has contributed an entropy increase of about $10^{40} J/K$
+
Show that the Sun has contributed the entropy increase of about $10^{40} J/K$
 
<div class="NavFrame collapsed">
 
<div class="NavFrame collapsed">
 
   <div class="NavHead">solution</div>
 
   <div class="NavHead">solution</div>
 
   <div style="width:100%;" class="NavContent">
 
   <div style="width:100%;" class="NavContent">
     <p style="text-align: left;">The solar power is $\approx 4\times 10^{26} W$and the age of the Sun $\approx 5\times 10^{9} yr$. Solar surface temperature is$\approx 6\times 10^{3} K$. This values yield the entropy increase
+
     <p style="text-align: left;">The solar power is $\approx 4\times 10^{26} W$ and the age of the Sun $\approx 5\times 10^{9} yr$. Solar surface temperature is $\approx 6\times 10^{3} K$. These values yield the entropy increase
 
\[\Delta S=\frac{\Delta Q}{T} \approx \frac{4\times 10^{26} W\cdot 5\times 10^{9} \cdot 3\times 10^{7} \sec }{6\times 10^{3} \; K} \approx 10^{40} \, J/K\]  
 
\[\Delta S=\frac{\Delta Q}{T} \approx \frac{4\times 10^{26} W\cdot 5\times 10^{9} \cdot 3\times 10^{7} \sec }{6\times 10^{3} \; K} \approx 10^{40} \, J/K\]  
The mechanism of increase of entropy is emergence of new degrees of freedom, which came into being by producing about $7\times 10^{6} $photons emitted into space per nucleon subject to nucleosynthesis. Indeed, The number of created photons follows from the ratio of released nuclear energy per particle $\approx 7\, MeV$ to the energy of a visible photon $\approx 1\, eV$, corresponding to the solar surface temperature.</p>
+
The mechanism of this entropy increase is due to creation of new degrees of freedom, which came into being by producing about $7\times 10^{6} $photons emitted into space per each nucleon taking part in nucleosynthesis. Indeed, the number of created photons follows from the ratio of released nuclear energy per particle $\approx 7\, MeV$ to the energy of a visible photon $\approx 1\, eV$, corresponding to the solar surface temperature.</p>
 
   </div>
 
   </div>
 
</div></div>
 
</div></div>

Latest revision as of 17:09, 10 November 2012


If someone points out to you that your pet theory of the universe is in disagreement with Maxwell's equations---then so much the worse for Maxwell's equations. If it is found to be contradicted by observation---well these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.
Sir Arthur Stanley Eddington



Problem 1: the cold of space

When designing a suit for open space, what should engineers be more careful of: heating or heat extraction?



Problem 2: calculating photons

Estimate a number of photons in a gas oven at room temperature and at maximum heat.



Problem 3: equilibrium

Estimate the temperature at the surface of the Sun, assuming that the Earth with mean temperature at its surface $15\,C^\circ$ is in thermal equilibrium with the Sun.



Problem 4: entropy of gravity

What is the difference between entropy of gravitational degrees of freedom and ordinary entropy (e.g., entropy of ideal gas)?



Problem 5: the Sun as the source of low entropy

One of the most used classifications divide physical systems into open and isolated. The entropy in an isolated system can only increase, eventually reaching the maximum at thermal equilibrium. In contrast, in open systems the entropy can decrease due to external interactions, for example, through absorption of a component with low entropy. Explain why the Sun is a source of low entropy for the Earth.



Problem 6: infrared vs ultraviolet photons

Estimate how many infrared photons Earth radiates per one ultraviolet photon it absorbs from the Sub.



Problem 7: entropy gain of the Universe per person

A human during his lifetime increases the entropy of the Universe by converting chemical energy contained in the food to heat. Estimate the corresponding entropy gain.



Problem 8: Earth's entropy production

Estimate the contribution of Earth during its existence to the entropy production.



Problem 9: Sun's entropy production

Show that the Sun has contributed the entropy increase of about $10^{40} J/K$