How long would the earth take to freeze abscent of the sun

[Alan McDougall]

Greatings I am new?

 

My question is east to stated but more difficult to answer (accurately)

 

Assume we could remove the earth from any other heat source in the universe. Leave it somewhere in a hypothetical totally empty vacuum , except for itself of course

 

How long would it take the earth, to dissipate all its heat by entropy, and freeze down to absolute zero, right down to its iron core

 

Peace Alan

[Phi for All]

Is it assumed that the ambient temperature of this "hypothetical totally empty vacuum" is already absolute zero?

[J.C.MacSwell]

Is it assumed that the ambient temperature of this "hypothetical totally empty vacuum" is already absolute zero?

 

That way it would make the answer an infinite amount of time, rather than many, many times that.

[Sisyphus]

Surely the answer is never?

[Alan McDougall]

Surely the answer is never?

 

Why never", I know absolute zero cant happen, but the earth could cool down in a trillion trillion google years to just a tiny fraction of absolute zero,

 

Even hadrons must ultimately decay and vanish in an estimated 35 00000000000000000000000000000000000000000000000000000000 years

[Phi for All]

Why never", I know absolute zero cant happen, but the earth could cool down in a trillion trillion google years to just a tiny fraction of absolute zero

But that's not what you asked in the opening post.

[swansont]

Absolute zero is not attainable in a finite number of processes, even in an unphysical scenario such as described.

[Alan McDougall]

Absolute zero is not attainable in a finite number of processes, even in an unphysical scenario such as described.

 

 

OK assume the void in which the earth finds itself in is absoloute zero, how long would it take for the earth to dissipate all its energy, reach total entropy and freeze solid

 

Come on guys you know what I mean, total decay

 

Alan

[J.C.MacSwell]

OK assume the void in which the earth finds itself in is absoloute zero, how long would it take for the earth to dissipate all its energy, reach total entropy and freeze solid

 

Come on guys you know what I mean, total decay

 

Alan

 

How long to lose half it's energy would be easier to define.

[Alan McDougall]

How long to lose half it's energy would be easier to define.

 

OK lets try half?

[swansont]

OK lets try half?

 

That's a bit easier to do. Estimate the thermal content. Use the Stefan-Boltzmann law to find out how much power we are radiating. Then integrate to see how long it will take to radiate away that much energy. That won't account for the transport time within the planet, but it'll give you a first-order approximation.

[John Cuthber]

Don't forget to account for radioactive heating.

[swansont]

Don't forget to account for radioactive heating.

 

I assumed we were ignoring that, but if not, then it's a killer for the original proposition.

[Alan McDougall]

I assumed we were ignoring that, but if not, then it's a killer for the original proposition.

 

Lets ignore nuclear heat and consider only geothermal heat for the time being

 

If we bring nuclear generated heat, think about how long the huge USA aircraft carriers can run without refueling, it is about twenty years, and of course the waste plutonium could also be utilizes later

 

For the earth to use all its nuclear fuel extrapolate that into eternity

[insane_alien]

alan, the 'nuclear heat' is heat generated by nuclear deacay of elements withing the earth. it is not the same as a fission reactor(although there have been at least two natural fission reactors).

 

to not include it means to not consider the earth at all.

[Alan McDougall]

alan, the 'nuclear heat' is heat generated by nuclear deacay of elements withing the earth. it is not the same as a fission reactor(although there have been at least two natural fission reactors).

 

to not include it means to not consider the earth at all.

 

Acknowledged , fission fusion what ever the source of energy lets keep it simple and go from there

 

Geothermal, and other heat also originates from the mantle, crust, oceans, core all these store colossal amounts of heat

 

Maybe we should narrow the thread down a little, how long could we survive if the sun went out tomorrow??

 

Peace to insane Alien

[cameron marical]

Surely the answer is never?

 

Why would It be never?

[CaptainPanic]

Apart from the fact that we'll never reach the absolute zero... because cooling is happening asymptotically (we would get closer and closer to zero, but earth (or any other object) would never really get there).

 

The issue is of course heat transfer. We know the current rate of cooling/heating. We know that we basically radiate as much heat as our sun sends to us.

 

Once there is no sun, the outside of the earth will initially cool at the current rate. Once it's cold, it will still cool (relatively) fast. The atmosphere would cool, oceans would freeze. And then the inside of the earth is still hundreds / thousands degrees. This heat from inside would need to go through all the layers and finally radiate into empty space (as infrared radiation).

 

It was already mentioned that radioactive decay will actually heat the planet.

In addition, the heat transfer that I just described takes place below the surface. We don't know what's going on there... and I don't even want to make a start at estimating all the parameters.

[swansont]

This heat from inside would need to go through all the layers and finally radiate into empty space (as infrared radiation).

 

Radiant heat should not be equated with infrared. Something at everyday temperatures radiates strongly in the IR. But of it's hotter, it radiates strongly in the visible (like the sun, or a stove burner or incandescent light bulb), and if it's cooler it will radiate in the microwave/RF. It's a spectrum, though — even very hot things radiate some in the RF.

 

So after the earth cooled in this scenario, it would be radiating at longer and longer wavelengths.

[CaptainPanic]

Radiant heat should not be equated with infrared. Something at everyday temperatures radiates strongly in the IR. But of it's hotter, it radiates strongly in the visible (like the sun, or a stove burner or incandescent light bulb), and if it's cooler it will radiate in the microwave/RF. It's a spectrum, though — even very hot things radiate some in the RF.

 

So after the earth cooled in this scenario, it would be radiating at longer and longer wavelengths.

 

Thanks. You're right. Wavelength and temperature are related there... and they don't radiate one very specific wavelength, but more a temperature (and material?) dependent spectrum.

 

But here on earth, IR is the major contributor to cooling. Once the earth would cool more, indeed other radiation would become more important.

[norefillsx]

without the sun, i think our planet would freeze completly in a few seconds...

[J.C.MacSwell]

without the sun, i think our planet would freeze completly in a few seconds...

 

Based on?

[CaptainPanic]

without the sun, i think our planet would freeze completly in a few seconds...

 

I think you're completely wrong there.

 

The atmosphere is a pretty good insulation. Cooling would be as fast as in the night. Some areas might freeze within hours, some will take days/weeks (depends on temperature when the sun suddenly vanishes, humidity, clouds, trees, geology, wind).

 

The influence of the sun on the temperature on the night-side of the earth is negligible... and I see no reason why cooling would speed up when the sun is gone completely suddenly.

 

The areas around the equator would take several days or even weeks to cool below zero (Celsius). A week is 7*24*3600 = 604 800 seconds. So I hereby claim that your "thought" was off by a factor of at least 100000.

[Phi for All]

I think you're completely wrong there.

I agree. Can you imagine interior molten magma freezing in seconds just because the sun shuts off, even if you remove the atmosphere as well?

[swansont]

A perfect blackbody 6400 km in radius at 300 K surface temperature will radiate 2.36e17 Watts. If the earth has a specific heat capacity of 1 kJ/kg-K and is uniformly at 300 K (which it isn't), it would take 3 months to radiate away that much energy — if the radiation rate stayed constant, which it won't because it varies as T^4, and ignores the time it would take to conduct heat to the surface. This assumes no incoming radiation at all.

 

All this tells you is an exceedingly conservative lower bound, and is more indicative of a time constant for a power-law decay, which would be measured in months or years or longer, depending on how bad the assumptions were and what is meant by "freeze completely."