What is the energy required to approach near absolute zero?

[shintashi]

TL;DR

is the scale linear or exponential?

I'm trying to understand if the amount of effort/energy required to get to absolute zero approaches infinity, or if its a linear thing... is there a point in which dropping near 0 kelvin changes from a 1:1 to an exponential curve? Is the whole thing a curve or is there a static point, like 1 degree kelvin is 1 joule different from 2 kelvin, but for whatever reason, 0.5 kelvin takes like a power plant?

I couldn't find anything explaining the curve, unlike approaching the speed of light, which is pretty straight forward and easy to find.

 

[hutchphd]

What is effort/energy.?? A coherent answer requires a specific and well thought out question. You should quote sources for your suppositions and be specific. Asking a good question is half the battle for understanding. Its your half.

 

[sophiecentaur]

A coherent answer requires a specific and well thought out question.

That's right, in principle but many people do not know enough for a well (enough for you) though out question. I know that's unsatisfying for the cognoscenti but one of PF's missions is to help people to access their 'unknown unknowns'. I feel that I understand what the OP is getting at (and I believe you actually do have a clue). The OP needs a bit of help across the line, I think.

@shintashi Most refrigeration is achieved in the region of 300K and your average refrigerating machine can manage one particular temperature difference, wherever it starts. I found this elderly article which is interesting and is based on thermodynamic ideas It points out that the energy needed is linear as you increase the ambient temperature but non-linear as you reduce the target temperature. You can do better than that by using other (non thermodynamic) methods like laser cooling this
Scientific American article is interesting. Read them both; they are good fun.

 

[etotheipi]

Why don't you try and figure out how much work you need to do for a refrigerator undergoing an ideal Carnot cycle? You can write some equations,$$\frac{Q_C}{T_C} = \frac{Q_H}{T_H}$$Use that $W + Q_C = Q_H$, and try and eliminate $Q_H$ to determine what $W$ corresponds to remove an amount $Q_C$ of heat from the cold reservoir, in terms of $T_C$ (and $T_H$). You will find that as you approach $T_C \rightarrow 0\text{K}$ this will become infinite.

 

[Vanadium 50]

That's right, in principle but many people do not know enough for a well (enough for you) though out question

The OP has been here for 17 years. I'd like to think that's enough.

 

[sophiecentaur]

The OP has been here for 17 years. I'd like to think that's enough.

Funny thing is that I understood his problem. But I guess I hope/ expect people to make allowances for my dumbness and it works both ways. Not to say that I’m never grumpy.