# Homework Assignment # 2 1 carbon dioxide snow on mars

 Дата канвертавання 22.04.2016 Памер 18.66 Kb.
SPU 30 – Life as a Planetary Phenomenon (Spring 2011)

Instructor: Dimitar Sasselov

## SOLUTIONS

Homework Assignment # 2

1) CARBON DIOXIDE SNOW ON MARS:

The total mass of the Earth's atmosphere is 5x 1018 kg, while the Martian atmosphere is about 1/150 the mass of Earth's atmosphere and is composed mainly (95 percent) of carbon dioxide.

(a) Estimate the total mass of carbon dioxide in the atmosphere of Mars and compare to the total mass of carbon dioxide in Earth's atmosphere.

5 x 1018 kg / 150 = 3.33 x 1016 kg = Mass of the entire atmosphere of Mars

3.33 x 10 16 kg * 0.95 = 3.16 x 1016 kg = Mass of CO2 in Mars' atmosphere
Given Earth's atmosphere contains approximately 0.0587% CO2 by mass
5x1018 * 0.000587 = 2.935 x 1015 kg = Mass of CO2 in Earth's atmosphere
Observations: There is just over 10 times as much CO2 in all of Mars' atmosphere than the CO2 in Earth's atmosphere, which is somewhat suggestive of how thin Mars' atmosphere really is, since CO2 is merely a trace gas on Earth and yet the two answers come out only one "order of magnitude" (a.k.a. factor of ten) apart.
(b) Compare your answer in (a) with the mass of a seasonal polar cap on Mars, approximated as a circular sheet of frozen carbon dioxide ("dry ice", having a density of 1600 kg/m^3) of diameter 3000 km and thickness 1 m. [Hint: use formula for the volume of a cylinder.]
Given: Diameter = 3000 km

Radius = 1500 km = 1,500,000 m

Volume of a cylinder = pi * R2 * h
Vol = 3.14 * (1,500,000 m)2 * (1 m) = 7.065 x 1012 m3
Density = Mass/Volume

Rearrange: Mass = Density*Volume

Mass = ( 1600 kg/m3 ) * ( 7.065 x 1012 m3 ) = 1.13 x 1016 kg
Observations: This answer is about one third of the answer found in part 1a for the mass of CO2 in Mars' total atmosphere, which is actually quite remarkable. This is saying that every Martian southern winter, 1/3rd of its atmosphere freezes out onto the southern polar cap... then in southern summer this turns back into vapor and travels north and freezes out on the northern polar cap. Every season this polar CO2 layer flips... and it is 1/3rd of the entire atmosphere moving back and forth! Nothing even remotely like this happens on Earth. Just another example of what a strange world Mars can be.

2) VENUS CLIMATE:
(a) Why did Venus dry up: (this is much more text than was needed, but we looked for many of the points here in the 4-5 sentences asked for. )

- Venus is believed to have initially formed very similar to Earth, in terms of both mass and composition, with a similar amount of initial water, which came from a similar bombardment of comets, as in the problem in homework 1.

- Venus's closer proximity to the sun is enough to explain only a few dozen degrees elevation in surface temperature relative to Earth, but nothing even close to the ~700K surface temperature seen today.
- But, the modest surface temperature elevation can be the trigger to starting a "runaway greenhouse effect", which works as follows:
- A greenhouse effect is a warming of a planetary surface that occurs because certain gases are very effective at absorbing certain wavelengths of light, in particular IR light (heat) which is re-radiated from a planet's surface (or a middle cloud layer) after visible wavelength light comes down from the sun and heats that surface up. Re-absorbing the outgoing IR radiation slows down the escape of solar energy, and acts like an insulating blanket, such that the bottom layers can become very warm. (note, all the energy does escape eventually, just by a "more resistant" route, so the planet doesn't become infinitely hot!)
- CO2 is the most famous "greenhouse gas" but not the most absorbing. (The strength of IR absorption of a given molecule type depends on the width and depth of its absorption bands in the IR range). In fact, one of the most powerful greenhouse gases, is H2O, or water vapor. (Methane, CH4 gas, is also a strong greenhouse absorber)
- The potency of H2O as a greenhouse gas causes the runaway effect on Venus.
- First Venus either has very early oceans or seas, or at least lots of water vapor in its atmosphere.
- An H2O amplified greenhouse evaporates more water. That amplifies the greenhouse even further in a strong "positive feedback" loop.
- Eventually you have all surface water on Venus evaporated and in the sky. But it is still water.
- The next key step, is sunlight. Over millions of years, H2O molecules near the top of Venus's atmosphere are exposed to solar radiation, which can break the molecules apart (a process called "photodissociation".)
- This is caused especially by UV radiation. This photodissociation rate occurs faster on Venus than it might on Earth because Venus is closer to the sun and thus has more intense UV light. Note: a lack of an Ozone layer on Venus would allow UV to reach lower atmospheric layers, as well as just the top, however... the early Earth did not have an Ozone layer either, until photosynthetic life evolved, so this alone does not cause the drying.
- You end up with H2O being converted into separated Oxygen and Hydrogen. Crucially, Hydrogen gas is light enough to escape the planet's gravity on its own, and float away into space (this is why Earth has no H2 gas in our atmosphere). Without a balanced amount of hydrogen to recombine with remaining, there is no way, if the planet were ever to cool again, for to the oxygen to recombine to create H2O again. The planet is now officially becoming "dry".

Example 4-5 sentence version:

Venus likely formed with similar amounts of water to Earth. Its closer position to the sun led to a moderate initial elevation in surface temperature which caused increased evaporation. H2O is a strong greenhouse gas (a gas that absorbs outgoing IR radiation, acting like an insulating blanket), therefore this evaporation, in conjunction with large amounts of CO2 in the atmosphere, continued to heat the surface in a "runaway greenhouse effect" positive feedback loop, until all H2O was in vapor form. Solar radiation then broke apart water molecules, at a faster rate than would happen at Earth, and hydrogen was able to the escape the planet, permanently destroying the original water.

Extra items:
- The free oxygen is highly reactive, and eventually reacts with surface rocks, and it too is lost from the atmosphere. Because Venus also (probably) lost its magnetic field early (or never had one), that makes the atmosphere vulnerable to "stripping" by high energy solar wind particles, which may also have removed some oxygen.
- The remaining atmospheric gases, are largely those that continue to "outgas" from the planet... especially CO2 from volcanoes.
- The fact that CO2 is also a greenhouse gas, even if not as strong as H2O vapor is, means that the planet does not cool back down to any "normal" greenhouse free state, just because the H2O vapor is steadily vanishing.
- Much of the outgassed CO2 on Earth has become locked up in carbonate rocks (limestone) at the bottom of our oceans, but this requires liquid water to occur. So again, just one more positive feedback as the oceans were drying, kept the process from halting.

(b) What keeps the surface of Venus so hot today?

- Fast forward 3-4 billion years: Venus is hot today (with a surface temperature of over 700 degrees Kelvin) because of a continuously occurring, and very strong  "steady state" greenhouse effect, generated by a thick atmosphere of mostly CO2 gas, as with the concern for global warming on Earth. CO2 gas absorbs light across wide wavelength bands of outgoing Infrared (IR) light, and acts like an insulating blanket, keeping the bottom layers very hot.

- If not explained in part (a), a brief explanation of what the term "greenhouse effect meant" means or how it works was looked for here.
- Unlike the "runaway greenhouse effect" that started this process and evaporated Venus's oceans early on, this greenhouse effect now maintains a constant temperature, and does not get worse with time, because the amount of CO2 is roughly constant with time.

Extra items:
- The CO2 does not decrease, as it does not Earth, by being absorbed into carbon-bearing rocks, because on Earth, this mainly occurs through liquid water chemistry in our oceans (creating limestone, e.g. chalk, or the White Cliffs of Dover.)
-  Photodissociation of CO2 does not work the way it does for water, because both C and O are heavy enough to not freely escape the gravity of the planet, and thus can recombine later. Volcanoes (if still active on Venus) release CO2 as one main component, which may replace any smaller ongoing losses of C and O to solar wind stripping
Note: the difference between part (a) and part (b) is mainly timing. (a): a runway water vapor amplified greenhouse, happened once, very early on. (b) is still occurring today, and is now steady-state.
(c)
Given: Atmospheric pressure of Venus = 9 x 106 Pa

- Boiling point of water on Venus ~ 570 K

(570 K = 297 degrees C (can subtract 273 degrees to convert K to C)

(Note: the "degrees symbol" is generally not used for Kelvin scale values)

- Venus surface temperature ~ 730 K, or ~ 457 degrees C (approximate values ok)

- Therefore on the present surface of Venus, despite the extremely high atmospheric pressure due to a thick CO2 atmosphere making it easier for water to remain liquid even at temperatures as high as 570 K, the greenhouse-induced temperature is still far too high for any liquid water to ever condense.

(d)
Earth's boiling point: 2 ways to plot.

1: Can say we know Earth's pressure is 92 times less than Venus, as stated in the problem.

9 x 106 Pa / 92 = 9.78 x 104 Pa

(about two orders of magnitude (100x) less, so should be about two major divisions (10x per major division) down on the exponential graph.

Answer comes out very close to 373 K, or 100 degrees C
2: Can just say we know the sea level boiling temperature of water is (and is the definition for) 100 C, and is therefore 100+273 = 373 K. Then go up on the graph from 373 K to plot the mark.

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