Martian Carbon Dioxide Turbine Oxygen Generator

Question

How much solid Carbon Dioxide can be collected in a container with the top of the container level with the ground during a Martian Winter? Side Question: What do you call a generator that runs on the seasons of the year?

At the end of the winter with the container ideally full and capped. During middle summer the container warms melting the solid carbon dioxide creating pressure.

How much pressure can be acquired this way in a year to turn a generator that runs an electrical arc or devise to crack carbon dioxide? The oxygen from cracked carbon dioxide would rise to the top of the container to be collected. Enough atmospheric pressure from the oxygen would keep the carbon dioxide as liquid separate from the Oxygen. Cracking carbon dioxide would create more heat and pressure inside the container to power the generator more.

Can enough ice collect at night to create a generator that runs one cycle per day instead of per year?

After the liquid carbon dioxide runs out how much oxygen would be left in the container?

Could the ice be mined to run this? Can a machine process and run on $CO_2$ and $H_2O$ for an $O_2$ by product?

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I have combined the question with another question that was about to be marked as a duplicate for they were very similar. I apologize for the inconvenience if you have to add to your answer. Answers should still be valid.

https://astronomy.stackexchange.com/questions/28232/how-thick-or-deep-does-solid-carbon-dioxide-accumulate-on-mars

Answer 1

Yes, in principle to both questions, why not? However we can calculate the maximum energy you could get from the generator. The vapour pressure of $CO_2$ at 0C is around 4MPa, so in a perfect world, you get a volume expansion of about $4 MPa/600Pa$ or 6400.

The formula for the work per mole done by isothermal expansion of a gas is

$$RT\mathop{\mathrm{ln}}(V_{final}/V_{init})$$

which here gives us roughly $8.6 kJ/mol$, much less than the roughly 1600 $kJ/mol$ needed to break both the carbon-oxygen bonds in $CO_2$.

So, assuming a perfectly efficient electrical generator and cracker (that produced no waste heat), you would have enough energy to crack roughly 0.5% ($8.6/1600$) of the $CO_2$ you trapped. That produces 32 g of oxygen and 12g of carbon from 44g of $CO_2$, using the power generated by about 10kg of $CO_2$ escaping through your turbine.

This article seems very relevant to the question of using electrical energy (whether from this type of turbine, or wind, solar or nuclear) to extract oxygen from $CO_2$. The work looks promising, but is currently at a very early stage, requiring expensive catalysts, a supply of water, very pure $CO_2$ etc. Efficiency is relatively good, but still not 100% and the products are $O_2$ and $CO$. This means that some oxygen is "wasted" as CO, but on the other hand much less energy is needed to do this conversion, so a larger fraction of the $CO_2$ can be cracked. Based on the same rough approximation as a above, 10kg of $CO_2$ trapped could create perhaps 160g of oxygen assuming perfect efficiency. Realistically, considerably less.

In practice, there are additional formidable challenges. A surface exposed to space in the Martian winter night will be cold enough for $CO_2$ to condense on it, but (a) you'd need to blow a lot of thin Martian air over the surface and (b) you'd need to remove and radiate away the latent heat released by the $CO_2$ as it solidifies. Otherwise you'd just get a very thin layer. Then you need to recover the energy efficiently from a flow of extremely low-density gas and find a very efficient chemical solution to "unburning" carbon. You'd also need to allow the liquid $CO_2$ to warm up as the evaporation into your generator cools it, which will limit the power you can extract.

Note: This replaces my previous answer which used the wrong formula for the energy released by the expanding gas, leading to a severely wrong final answer