Thermo warm-up - Revision history

Igor: /* Problem 9: Sun and entropy production */

2012-11-10T17:09:57Z

‎Problem 9: Sun and entropy production

Igor: /* Problem 8: Earth and entropy production */

2012-11-10T17:05:03Z

‎Problem 8: Earth and entropy production

Igor: /* Problem 7: person and entropy of the Universe */

2012-11-10T17:04:00Z

‎Problem 7: person and entropy of the Universe

Igor: /* Problem 6: "infrared" and "ultraviolet" photon */

2012-11-10T17:01:10Z

‎Problem 6: "infrared" and "ultraviolet" photon

Cosmo All at 17:56, 5 November 2012

2012-11-05T17:56:49Z

Cosmo All at 17:30, 5 November 2012

2012-11-05T17:30:09Z

Cosmo All: /* Problem 7: person and entropy of the Universe */

2012-11-05T17:24:33Z

‎Problem 7: person and entropy of the Universe

Cosmo All at 17:23, 5 November 2012

2012-11-05T17:23:50Z

Cosmo All at 16:43, 5 November 2012

2012-11-05T16:43:10Z

Igor: /* Problem 5: the Sun as the source of low entropy */

2012-10-11T15:16:06Z

‎Problem 5: the Sun as the source of low entropy

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-=== 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 $10^{40} J/K$
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-     <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
 \[\Delta S=\frac{\Delta Q}{T} \approx \frac{4\times 10^{26} W\cdot 5\times 10^{9} \cdot 3\times 10^{7} \sec }{6\times 10^{3} \; K} \approx 10^{40} \, J/K\]
-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>
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-=== Problem 8: Earth and entropy production ===
+=== Problem 8: Earth's entropy production ===
-Estimate contribution of Earth during its existence to the entropy production.
+Estimate the contribution of Earth during its existence to the entropy production.
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-     <p style="text-align: left;">This estimate is based on the incoming power $10^{3} \, W/m^{2} $ of solar radiation. The area of the Earth's surface is $S\approx 1.3\times 10^{14} m^{2} $ and the age of the Earth is  $\approx 5\times 10^{9} yr$.  So that the total received energy is about
+     <p style="text-align: left;">This estimate is based on the incoming power $10^{3} \, W/m^{2} $ of solar radiation. The area of the Earth's surface is $S\approx 1.3\times 10^{14} m^{2} $ and the age of the Earth is  $\approx 5\times 10^{9} yr$.  Then the total received energy is about
 \[\Delta Q\approx 10^{3} Wm^{-2} \cdot 1.3\times 10^{14} m^{2} \cdot 5\times 10^{9} \cdot 3\times 10^{7} \sec \approx 2\times 10^{34} J\]
 The same amount of energy is released as heat at the Earth 's surface temperature of $T\approx 300\, K$,  yielding the entropy increase
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 === Problem 9: Sun and entropy production ===
 Show that the Sun has contributed an entropy increase of about $10^{40} J/K$

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-=== Problem 7: person and entropy of the Universe ===
+=== Problem 7: entropy gain of the Universe per person===
-A person during the lifetime increases the entropy of the Universe, converting the chemical energy contained in the food into heat energy. Estimate this value.
+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.
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-     <p style="text-align: left;">A simple estimate is based on the assumption that a person consumes about $2000\;kcal \approx 10^7 J$ in food per day for about $75\,yr$ and dissipates most of it as heat at $ \approx 300\,K$ Consequently, our contribution in the entropy production is \[\Delta S = \frac{\Delta Q}{T} \approx \frac{10^7 J \times 365 \times 75}{300\;K} \approx 10^9 \,J/K\]</p>
+     <p style="text-align: left;">A simple estimate is based on the assumption that one person consumes about $2000\;kcal \approx 10^7 J$ in food per day for about $75\,yr$ and dissipates most of it as heat at $ \approx 300\,K$ Consequently, our contribution in the entropy production is
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 === Problem 8: Earth and entropy production ===
 Estimate contribution of Earth during its existence to the entropy production.

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-=== Problem 6: "infrared" and "ultraviolet" photon ===
+=== Problem 6: infrared vs ultraviolet photons ===
-Estimate how many "infrared" photons per one "ultraviolet" photon.
+Estimate how many infrared photons Earth radiates per one ultraviolet photon it absorbs from the Sub.
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 === Problem 7: person and entropy of the Universe ===
 A person during the lifetime increases the entropy of the Universe, converting the chemical energy contained in the food into heat energy. Estimate this value.

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 \[\Delta S=\frac{\Delta Q}{T} \approx \frac{2\times 10^{34} J}{300\; K} \approx 10^{32} \, J/K\]
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      <p style="text-align: left;">The ratio of outcoming/incoming numbers of photons is equal to the ratio of the solar and Earth surface temperatures $ \approx 6000/300 \approx 20$
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 ''to the past:'' the low entropy component is a consequence of gravitational collapse during the creation of the Sun.</p>
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-     <p style="text-align: left;">The Earth return the same amount of energy to environment as it receive from the Sun. However, the form of energy from the Sun has considerably less entropy \underline{(sic!)}. Since absorbed "yellow" photons have more energy, than infrared photons of Earth's radiation, energy from the Sun is transmitted by smaller number of photons and, hence, smaller number of degrees of freedom and phase volume. As a result, Sun photons nave less entropy in comparison with photons, emitted by Earth.
+     <p style="text-align: left;">The Earth returns the same amount of energy to environment as it receives from the Sun. However, the photons coming from the Sun, that carry the same amount of energy, possess considerably less entropy: as the absorbed "yellow" photons are more energetic than the infrared photons of Earth's radiation, the energy from the Sun is transmitted by smaller number of photons and, hence, smaller number of degrees of freedom and phase volume. As a result, the Sun's photons have less entropy in comparison with the photons emitted by the Earth.
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 This chain could be continued both to the future and the past.
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-''to the future:'' plants use low entropy energy of the Sun in photosynthesis, thus reducing their entropy. We do the same when we eat plants or those, who eat plants.
+''to the future:'' plants use the" low entropy energy" of the Sun in photosynthesis, thus reducing their entropy. We do the same when we eat plants or those, who eat plants.
 <br/>
-''to the past:'' low entropy component is a consequence of gravitational collapse during generation of the Sun.</p>
+''to the past:'' the low entropy component is a consequence of gravitational collapse during the creation of the Sun.</p>
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