Kind of?
Despite what others said, temperature is not actually your problem. Pressure is. The pressure on surface is over 90 times what you want inside your habitats. Not to mention that pressure comes in the form of super critical carbon dioxide at 740 kelvins.
What this means is that the ratio of temperature difference is smaller than the ratio of pressure difference. So if you find a way to deal with the pressure, the heat won't be an issue.
I'd go for a plant that uses power to de-pressurize the supercritical carbon dioxide. Then give your habitat multiple pressurized shells with inner shells having progressively more survivable pressures. This is not mechanically as good as one shell but it would be easier to construct and if you fill the intermediate shells with de-pressurized carbon dioxide you will also get cooling "for free". For as long as the power plant works and carbon dioxide gets cycled anyway. You could also extract some water from the carbon dioxide. Probably not much but given that you'd want the habitat very well sealed anyway, maybe enough?
Some limitations on your power plant would apply though. If the power is produced with a heat engine of any kind or in general with a process that relies on temperature difference, you cannot use the cooling to create that temperature difference and then use the power produced to run the cooling. Well, you can, but you might have to name your colony the barony of Münchhausen for it to work.
Still, nuclear reactions can produce high enough temperatures for it to work even with cold end at 740 kelvins and other energy sources are possible. Maybe that supercritical carbon dioxide has flows that you can extract energy from?
In any case you'd probably need lots of power. And good redundancy with it.
The lava tubes are not really doing anything for you. Except trapping you underground and under a sea of supercritical carbon dioxide if things go wrong. I'd go for a rig or ship that floats in the carbon dioxide instead. Much easier to evacuate to those cloud top bases or to supply or build. And it can be moved.
11Temperatures are going to increase as you go deeper, not decrease. – Arkenstein XII – 2019-05-16T01:07:01.703
@ArkensteinXII I mean that as in "What area would you have to be in in it's interior to hit the 'Sweet spot'?" – Greenie E. - Reinstate Monica – 2019-05-16T01:08:54.690
2The surface of Venus is already 462 degrees Celsius, and therefore uninhabitable. It gets hotter from there... – Arkenstein XII – 2019-05-16T01:18:23.660
I want a way to do this.... – Willk – 2019-05-16T01:39:28.907
13You can live anywhere you want if you don't care about how long that life is. – Giter – 2019-05-16T02:10:50.010
1@Willk The way to do it is with brute-force refrigeration. – Logan R. Kearsley – 2019-05-16T04:00:03.320
1@LoganR.Kearsley refrigeration works by transferring heat from a hot place to a colder one. You cannot refrigerate without a cold place to dump the heat in. – JFL – 2019-05-16T09:28:25.890
@JFL You could dump it anywhere you want on Venus. There is no one to care if you pollute the atmosphere/blast hotter air out a gigantic fan. Of course the challenges to make a functional refrigeration system on Venus are so many I don't even know where to start... – conman – 2019-05-16T10:08:26.897
1@comman I think you missed the point. If you want to refrigerate a place to 20°C you need another place that is not too far away from 20°C . Such a place doesn't exist on Venus (except in upper atmosphere, but then you have interesting engineering challenges...) – JFL – 2019-05-16T10:37:20.027
2@JFL So if I want to, say, refrigerate a place to 4°C, I need another place not too far from 4°C to dump the heat ? I'm afraid my fridge is breaking physics then. – Keelhaul – 2019-05-16T11:53:12.610
2@JFL larger temperature differences are certainly much harder, and you might end up with pitifully low efficiencies in your system. The fact that we manage to cool things on earth (~300K) to microkelvins suggests that there isn't a hard limit. Whether or not cooling that substantial on a scale large enough to support life is possible is a different (engineering) question, and it may be practically impossible. However, there is nothing in the law of physics that prevents it, presuming you have enough energy to do the work. – conman – 2019-05-16T12:15:45.223
1Agree that there's no hard limit, and indeed this is more an engineering question. I badly phrased it, but I believe that considering the Delta-T involved this is not doable in practice. The math would be interesting tough. – JFL – 2019-05-16T12:22:08.463
3@JFL The very first line on the Wikipedia article about refrigeration is "Refrigeration is a process of removing heat from a low-temperature reservoir and transferring it to a high-temperature reservoir." Edit: To say that you phrased it badly is an understatement. – Fax – 2019-05-16T12:22:13.777