Ad: "Black Holes in the Universe"
The next seminar of the Balseiro Institute in Bariloche Atomic Centre will be delivered by Dr. Felix Mirabel.
Sunday, October 25, 2009
Is Keri Hilsons Hair A Weave
a planet's surface temperature, surface temperature
comes the end of our trilogy on the orbital temperature. In the first part
where $ \\ sigma $ is the constant Stefan-Boltzmann and $ \\ left (4 \\ pi R_ \\ Oplus ^ 2 \\ right) $ is the Earth's surface (here we consider the total surface of the Earth and not only its cross section as in the case of the energy absorbed .)
The equilibrium occurs when the energy absorbed is equal to the radiated energy. If there is an imbalance, the parameters are adjusted so as to reach a new condition. Suppose for example that for some reason increases the solar luminosity $ L_ \\ odot $. In this case, the energy that Earth receives will be greater and this leads to an increase in temperature, which implies an increase in the radiated energy. This equilibrium condition is therefore stable. Then:
\\ [E_ {abs} = E_ {emit} \\]
remember the expression for $ E_ {abs} $ obtained in the first part
and since brightness is energy per unit time,
\\ [L_ {abs} = \\ frac {L_ \\ odot} {4} \\ left (\\ frac {R_ \\ Oplus} {R_ {UA} \\ right) ^ 2} \\]
Therefore, our equilibrium condition occurs when:
\\ [L_ {abs} = L_ {emit} \\]
\\ [ \\ frac {L_ \\ odot} {4} \\ left (\\ frac {R_ \\ Oplus} {R_ {UA} \\ right) ^ 2} = \\ Left (4 \\ pi R_ \\ Oplus ^ 2 \\ right) \\ sigma T_ \\ Oplus ^ 4 \\]
and then clearing the temperature $ T_ \\ Oplus $ we have:
\\ [T_ \\ Oplus = \\ sqrt [4] {\\ frac {L_ \\ odot} {16 \\ pi \\ sigma} \\ frac {1} {R_ {UA} ^ 2}} \\]
Before numbers forward some conclusions:
The temperature is independent of the size of the planet (note that $ R_ \\ $ Oplus canceled) increases with the fourth root of the solar luminosity, and decreases with square root distance.
The equation is valid for any star-planet system, and is used inter alia to determine the "
\\ [T_ \\ Oplus = \\ sqrt [4] {\\ frac {3.85 \\ times 10 ^ {26} \\ mathrm {W}} {(16 \\ pi) (5.67 \\ times 10 ^ {-8} \\ mathrm {W} \\ mathrm {m} ^ {-2} \\ mathrm {K} ^ {-4}) (1.5 \\ times 10 ^ {11} \\ mathrm {m}) ^ 2}} \\] \\ [T_ \\ Oplus = 278 \\ mathrm {K} = 5 ^ \\ mathrm {o} \\ mathrm {C} \\]
comes the end of our trilogy on the orbital temperature. In the first part
, we calculate the solar energy that Earth receives, and the second part
, which would estimate the temperature of the Earth if the Sun was not calculate In this third part (last !) the equilibrium temperature. We have already determined that every second the earth receives $ 1.74 \\ times 10 ^ {17} $ J. What does the Earth with this energy? In short, it is heated. And we know that a hot body radiates energy according to the Stefan-Boltzmann (radiated energy increases with the fourth power of the temperature!). Suppose that the Earth has a temperature $ T_ \\ Oplus $ and behaves as a black body (a more reasonable assumption at this level), then the power radiated into space (usually using the letter $ L $ per light) is: where $ \\ sigma $ is the constant Stefan-Boltzmann and $ \\ left (4 \\ pi R_ \\ Oplus ^ 2 \\ right) $ is the Earth's surface (here we consider the total surface of the Earth and not only its cross section as in the case of the energy absorbed .)
The equilibrium occurs when the energy absorbed is equal to the radiated energy. If there is an imbalance, the parameters are adjusted so as to reach a new condition. Suppose for example that for some reason increases the solar luminosity $ L_ \\ odot $. In this case, the energy that Earth receives will be greater and this leads to an increase in temperature, which implies an increase in the radiated energy. This equilibrium condition is therefore stable. Then:
\\ [E_ {abs} = E_ {emit} \\]
remember the expression for $ E_ {abs} $ obtained in the first part
:
\\ [E_ {abs} = \\ frac {L_ \\ odot t} {4} \\ left (\\ frac {R_ \\ Oplus} {R_ {UA} \\ right) ^ 2} \\]
and since brightness is energy per unit time,
\\ [L_ {abs} = \\ frac {L_ \\ odot} {4} \\ left (\\ frac {R_ \\ Oplus} {R_ {UA} \\ right) ^ 2} \\]
Therefore, our equilibrium condition occurs when:
\\ [L_ {abs} = L_ {emit} \\]
\\ [ \\ frac {L_ \\ odot} {4} \\ left (\\ frac {R_ \\ Oplus} {R_ {UA} \\ right) ^ 2} = \\ Left (4 \\ pi R_ \\ Oplus ^ 2 \\ right) \\ sigma T_ \\ Oplus ^ 4 \\]
and then clearing the temperature $ T_ \\ Oplus $ we have:
\\ [T_ \\ Oplus = \\ sqrt [4] {\\ frac {L_ \\ odot} {16 \\ pi \\ sigma} \\ frac {1} {R_ {UA} ^ 2}} \\]
The temperature is independent of the size of the planet (note that $ R_ \\ $ Oplus canceled)

\\ [T_ \\ Oplus = \\ sqrt [4] {\\ frac {3.85 \\ times 10 ^ {26} \\ mathrm {W}} {(16 \\ pi) (5.67 \\ times 10 ^ {-8} \\ mathrm {W} \\ mathrm {m} ^ {-2} \\ mathrm {K} ^ {-4}) (1.5 \\ times 10 ^ {11} \\ mathrm {m}) ^ 2}} \\]
more impressive results, is not it?
Thursday, October 22, 2009
Franklin Mint Vase Butterflies
3rd part of a planet, part 2
say that sequels are never good, but we will make the attempt ...
In the first part say that sequels are never good, but we will make the attempt ...
course to answer this question we must first define what it means "Empty space." Strictly speaking, the empty space there. And for various reasons: cosmology, quantum and relativistic. Re-ask: At what temperature is a region of space with no stars or other energy sources nearby?
(yes, as the oven!), Which extend in the electromagnetic spectrum between 300 MHz and 300 GHz

Alpher and R.
Hermann
, and was discovered (by accident) in 1965 by Hermann
A. Penzias and R. Wilson (Nobel Prize winners in 1978 for this work) is actually a relic of the Big Bang to the time when the universe became transparent to radiation, or put another way, when finally electrons and photons allowed to interact and electrons began to form atoms with the baryons. From that moment (about 300,000 years after the Big Bang), the photons propagate through the expanding Universe with almost no interaction (the current density is 410 photons per cubic cm.)
And since the universe expands adiabatically (by definition, the universe is a closed system), the temperature of this background radiation decreases as time progresses. The current temperature of the background radiation was measured with extreme accuracy (parts per million) and is 2.725 K, and its distribution corresponds to that of a black body at that temperature.
We finally have our answer: if the sun suddenly disappeared, and if the Earth had no nuclear processes inside, the temperature of the Earth gradually fall to reach thermal equilibrium with the background, about 2.7 K (about -270 ° C).
continued ...
Subscribe to:
Posts (Atom)