At what distance would a Venus-like planet have a HZ temperature?

[xpell]

TL;DR

Approximately, at what distance from the Sun would a Venus-like planet have a habitable zone surface temperature? (A "back-of-the-envelope" educated calculation is enough.)

Well... that: Please, could you please assist me in obtaining a rough estimate of the distance from the Sun at which a planet resembling Venus or a hypothetical Venus-like planet (for the sake of simplicity) would have a habitable-zone surface temperature? A "back-of-the-envelope" educated calculation is enough, I'm simply a curious individual pondering this question, but if you could provide additional details or guide me on how to perform such calculations independently (as I had to enter the workforce right after completing high school, many years ago...), you would help to brighten my day.

 

[hutchphd]

As stated, this is a very difficult question. The nonlinear processes which have made Venus so very hot (500C) are not easy to model.

So I will answer a much easier question "suppose the atmosphere and surface of venus were similar earth. How hot would it be". Using only simplest black body radiation equation $$P=(surface~area) \sigma T^4$$ to model radiant energy balance shows that the temperature on earth should from sunlight and reradiation be ~300K or ~30C which is (~) pretty close. Earth and Venus are the ~same size. Venus is R_V=70million miles from sun and the earth R_E~90million miles . $$\frac {P_V} {P_E}= ( {\frac {R_E} {R_V}})^2$$ and so $$(\frac {T_V} {T_E})^4= ( {\frac {R_E} {R_V}})^2$$ , $$ {T_V} = \sqrt {\frac {R_E} {R_V}}T_E =340K$$ which is far different. Carl Sagan did some of the early work pointing to greenhouse effect on Venus as the cause.

 

[xpell]

As stated, this is a very difficult question. The nonlinear processes which have made Venus so very hot (500C) are not easy to model. So I will answer a much easier question

Huh... OK, thank you, Hutch, but as you said, that's nothing to do with my question. I would have been able to calculate your answer myself without the need to ask here. Only that it's not an answer to my question, not even if a "back-of-the-envelope" roughly approximate answer using a "simplified Venus" as I suggested. I'd be OK with a "roughly 5 to 10 AU because of this and this"-type answer.

 

[hutchphd]

There is no such "simplified Venus". Sorry.
I could make up something useless if you really wish.............

 

[berkeman]

Huh... OK, thank you, Hutch, but as you said, that's nothing to do with my question. I would have been able to calculate your answer myself without the need to ask here. Only that it's not an answer to my question, not even if a "back-of-the-envelope" roughly approximate answer using a "simplified Venus" as I suggested. I'd be OK with a "roughly 5 to 10 AU because of this and this"-type answer.

I know little about the subject, but can you look at it from a different direction? How is the HZ calculated? Whoever has done those calculations must have done them for different types of planets, including ones like Venus, no?

 

[Vanadium 50]

One might respond that if the answers one gets from volunteers are not satisfactory, one is always free to go elsewhere. That is probably more likely to be helpful than complaining.

A 300K Venus looks very different from a 750K Venus. At that temperature, much (but not all) of the atmosphere will condense out into CO2 lakes. This affects its dynamics and it almost surely affects clouds, which in turn affects albedo.

 

[snorkack]

A 300K Venus looks very different from a 750K Venus. At that temperature, much (but not all) of the atmosphere will condense out into CO2 lakes. This affects its dynamics and it almost surely affects clouds, which in turn affects albedo.

Yes. The cloud effect on the albedo will be important.
Back of the envelope: at 300 K, the vapour pressure of CO₂ is 67 bar (More precisely, 67,33 bar at 27,22 C). It is 65,65 bar at 26,11 C and 69,02 bar at 28,33 C. Since the total stockpile of CO₂ on Venus is 92 bar, it will actually be a minority of atmosphere that rains out.
Note that the same effect:
diminish the sunlight incident on Venus, leave its spectrum unchanged, allow free escape of radiation from Venus
might be achieved either by moving the rocky body of Venus to a more distant orbit, or else by placing a partially transparent sunshade between Venus and Sun, far enough from Venus that it does not block escape of radiation.
So how do you calculate the required transmittance of sunshade to make Venus habitable, rather than too cold?

 

[hutchphd]

Since the total stockpile of CO2 on Venus is 92

How do we know this ? Reference please.

 

[snorkack]

How do we know this ? Reference please.

Checking up, slightly less. About 89 bar:
the total composition
https://nssdc.gsfc.nasa.gov/planetary/factsheet/venusfact.html
gives 92 bar as the total pressure, but 3,5% (3,2 bar) is other gases.
But the conclusion: that at 300 K, a minority of atmosphere rains out (67 bar out of 89 bar total) stands.

 

[hutchphd]

Since the total stockpile of CO2 on Venus is 92 bar, it will actually be a minority of atmosphere that rains out.

So I do not follow the significance here. There is thermal gradient in the existing atmosphere that influences the cloud elevation. Why is this salient?

 

[snorkack]

So I do not follow the significance here. There is thermal gradient in the existing atmosphere that influences the cloud elevation. Why is this salient?

To clarify the expression "much but not all" of the atmosphere, that will rain out.
At 300 K, a large fraction but not the majority of the atmosphere will rain out. At 305 K, nothing will rain out. At 283 K, most of the atmosphere will rain out.
What causes the sharp bottom of Venus´ cloud deck at 48 km altitude?

 

[Vanadium 50]

I don't know what snorkack is going on about.

The triple point of CO2 is at about 5 atmospheres and 230 K. So depending on what you call a "habitable" temperature, the pressure can be anywhere between 5 and ~50 atmospheres. Probably 20 or 30, which means 2/3 or 3/4 or so of the atmosphere will have condensed.

Will there be rain? Maybe.

Will the rocks outgas CO2? Maybe - depends on the chemistry. Note that for constamt temperature, this excess CO2 ends up in the lakes. (Which is part of the reason this is an unanswerable question - lots of dynamics)

Note also that as Venus goes farther out its solar day gets longer and longer. It is entirely possible that it never is in the habitable zone - the hot side is too hot and the cold side is too cold.

 

[hutchphd]

I can justify whatever @xpell wants.......I may become airborn from the hand waving, but just give me a number and I can get there.

 

[Vanadium 50]

Clearly 0.7 AU isn't enough, and 5 AU is surely too much, so pick some number in between. 2? 3? 4? Take your pick.

 

[snorkack]

I don't know what snorkack is going on about.

The triple point of CO2 is at about 5 atmospheres and 230 K.

More precisely 5.2 bars, 216.6 K.
And the triple point is 73.8 bars, 304.2 K

So depending on what you call a "habitable" temperature, the pressure can be anywhere between 5 and ~50 atmospheres. Probably 20 or 30, which means 2/3 or 3/4 or so of the atmosphere will have condensed.

Converting it back to temperature:
5 bar at -57 C
20 bar at -20 C
30 bar at -6 C
50 bar at +14 C
and...
67 bar at +27 C (300 K)
72 bar at +30 C
74 bar at +31 C critical point.

Will there be rain? Maybe.

Probably. There will be heat transfer. Where will the cooling/condensation leg be located?

Will the rocks outgas CO2? Maybe - depends on the chemistry.

Note that they have been thoroughly outgassed for a long time at +460 C. Which means cooling CO₂ to below 40 C would result is some reversal - some ingassing.

Note that for constamt temperature, this excess CO2 ends up in the lakes. (Which is part of the reason this is an unanswerable question - lots of dynamics)

Note also that as Venus goes farther out its solar day gets longer and longer. It is entirely possible that it never is in the habitable zone - the hot side is too hot and the cold side is too cold.

Near critical, dense gas is very efficient for heat transfer.
What would an ocean look like that has a non-shore at the critical point? That is, a body of fluid whose cold end is at 30 C and has a surface but whose warm end is at 32 C?