Water-cooled lander Options

[tanjent]

There is a recent posting on Emily's Planetary Society blog, which must be Doug's because she's not there herself, although her name is the only name on it. The subject is using water to cool a long-lived surface probe on Venus. It sounds far more practical than any of the other proposals for landing giant atomic-powered refrigerators, or developing a whole new family of high-temperature semiconductors, etc.

But I didn't understand the whispered criticism to the effect that the Ekonomov paper assumed that the water would absorb heat only from the one watt of power driving the instrument package itself. I simply can't believe that he went to the podium and presented his model without taking into account the fact that the surface of Venus is a pretty hot place, and that the proposed probe would be absorbing the ambient heat. This is an interesting proposal and I would like to understand both the original calculation of 50 days to bring the water to a boil, and the cited flaw in the calculation. I too find it hard to believe that it would take 50 days to bring water to a boil on the Venusian surface, but where exactly is the error, and what remains after we correct it?

Doug is busy of course, but I hope he will find the time to address this when he returns, if someone else hasn't done so by then.

[tty]

If we assume that 500 W is a realistic heat input what will happen?

This is very much a back-of-the-envelope calculation, mind you

I assume that we start with 100 kilos of ice at 273 K. To melt 1 gram of ice takes 333 J so 500 Watts will melt 1.5 grams of ice per second. It will take about 67000 seconds to melt 100 kilograms, so temperature will stay stable at 273 K for about 18 hours.
Temperature will then start rising more or less linearly as the water warms up. It takes 4.19 J to raise the temperature of one gram of water one degree. 500 Watts will therefore raise the temperature of about 120 grams of water one degree. So it will take about 830 seconds (slightly less than 14 minutes) for the water to heat up one degree. For the temperature to rise 100 degrees will thus take about 23 hours. However the water won't boil at 100 degrees since the steam can't vent into the atmosphere until the pressure is higher than atmospheric pressure. The phase diagram I have is logarithmic so it's a bit difficult to be sure but it seems that water boils at about 500 K on the surface of Venus. That temperature should be reached after about 50 hours. The water then starts boiling and vents to the atmosphere. It takes 2260 J to boil one gram of water so 500 Watts will boil about 0.22 grams of water per second. To boil away 100 kilos will then take about 450,000 seconds i e about 125 hours. The temperature will then quickly go to ambient.

So temperature should stay at 273 K for about 20 hours then rise to about 500 K over about 50 hours and then stay at 500 K for about 120 hours, altogether a little more than a week.

And yes, I'm aware that the constants I've used vary with temperature and that the heat flux is also dependent on the thermal gradient, and yes, the venting steam will actually cool the surroundings a little (and could probably be routed to maximize this effect).

P.S. It just struck me that by adding a pump to evacuate the steam you could have those 120 hours at 373 K rather than 500 K. It would have to be a very good pump though,