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Viewing Single Post From: The giant space ship example
gbaikie

Chris Ho-Stuart
 
That's a different question to the spaceship; it relates the magnitude of Earth's effective heat sink. This is dominated by the ocean. More seriously, the question must consider that as temperatures increase on a planet, it radiates more energy. If you have a very simply planet, like the starship, we can ignore "climate sensitivity" worries and just use the "Planck response".


I view it as way to check your answer. I not concerned about effective heat sink. Effective heat sink has nothing to do with spaceship as there is no night and day.
Though you do have figure out the atmosphere's effective heat sink to determine the speed in which the atmosphere will warm.

I will illustrate what I mean. Suppose we cover the planet in 2 meters water and freeze it so it's ice at 2 K.
With this done, I can add the 150 K air. And heat the air with these 6,580,000 GigaWatts reactors.
The ice I am not trying to directly heat, and I could basically ignore it. Because the air will take "forever" to warm it.
But the time it takes to warm the air will inform you about how much energy is needed.

In other words to take an extreme example, suppose these reactors heat the air and increase the temperature by 1 K an hour. Which would mean that in 10 hours [roughly] it would get 10 K warmer- or say 20 K per day. So roughly in one day atmosphere gains 20 K and ice might warm as much as 1 K [any increase in temperate of ice is a loss but the effort is focused on heating the air though such a cold surface could add some interesting dynamics. Also heating the atmosphere so rapidly would have "interesting dynamics"- it would be very turbulent- the warm air goes to top. Heating that quickly should give fairly uniform temperature [not desired-huge losses].
Now you could dampen the above mentioned losses. Insulate the ice and heat large quantities of air and mix within "furnace" so the exhaust in exits at near surface temperature and low air velocity- which is harder technically to do, but isn't the issue.

Or instead doing the frozen water thing. One could start with entire atmosphere in frozen state- have nuclear furnace circulate air thru huge ducts. Air exits reactor at 600 K or something and returns at 100 K to be reheated. Anyways- I am getting bogged down in whatever technology is used.

Chris Ho-Stuart
 
This is how it works.

For a surface at 150K, the thermal radiation is only 28.7 W/m^2. An additional 658,000 GW, spread out over Earth's surface area of 5.1e14 m2, means an extra 1.3 W/m2, so it enable the surface to radiate 30 W/m^2. That corresponds to a temperature of 152 K.


That doesn't seem right- you seem to be saying 2 K every second.

So, we got how much total atmosphere.
Your chart says: 2.16e22 and 5.4e17. I think it's the latter.
So 5.4e17 kg.
And need specif heat per kg of air at 150 K
".715 Joules per gram per degree Kelvin "
And:
Ok, it's about 1 kJ/kg.K
http://www.engineeringtoolbox.com/air-properties-d_156.html
So 5.4e17 KJ per K
Or 5.4e20 watts/joules And have 6,580,000 GigaWatts
Which is 6.58 x 10^15 watts
So about 100,000 seconds and one day is 86400 seconds
So 1 or two days per 1 K increase
You said "For a surface at 150K, the thermal radiation is only 28.7 W/m^2. An additional 658,000 GW"
Do mean requires 658,000 GW to maintain 150 K?
If so that allows 6,580,000 - 658,000 which is 5,922,000 GW to add heat when at 150 K, meaning less than 1 1/2 days to increase one K, and 15 days to get 10 K increase.

Now, if we continue to ignore the ground. What we need is average temperature of air- it could be near 150 K, though should be warmer.
Air at surface is 10 C [282 K]. If temperature drops by 1 K per 1000 meters at 100,000 meters
it's 182 K.
At what elevation is half the atmosphere?
Take average temperature for one half and take average temperature of other half- and average
both.
Or could simply count up to 100,000 meter [it has to be much higher than this]- and say average temperature is 282 minus 50 K which 232 K.
Then to continue with rough approximation, we could use heat pumps to cool the ground to 232 K
and don't have ignore the ground anymore.
The ground could like the cold concrete floor in a basement which can have warmer air above it.
Though without heat pumps drawing away heat from the ground this planet has been in blackness of universe for billions of years and don't have much internal heat and would stay cold for long time.
Or the 10 C air would in net, lose heat warming the ground and never get very far in this regard for centuries.
Edited by Chris Ho-Stuart, Dec 5 2011, 01:43 AM.
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The giant space ship example · Physical theory for climate