# What happens to a body, initially at 300K, kept in isolated space? Will it's temperature drop to 0k?

With regards to Thermal Radiation, given a stable body initially at 300 Kelvin placed in isolation, after continuous Thermal Radiation will it's temperature gradually reduce to 0 kelvin asymptotically? If so, does this mean that the body is now devoid of any Thermal Energy? And does it imply that the only energy it can possibly have is (now) due to it's electronic structure?

• Not zero but 2.7K
– Paul
Mar 31 '15 at 11:33
• I think that your question assumes that it is a black body radiation, that cools down the body. If you do the simulation by finite-range method, you have an asymptotic behavior and you reach zero in infinite time. However, Mar 31 '15 at 11:55
• However, in a physical world, there is a question - what is the process that enables to irradiate your energy. When approaching to zero, you irradiate longer and longer waves and I would guess, that at some moment the process will be hindered or even blocked. There are also other degrees of freedom, that create your temperature. Look at wiki, what is zero temperature. en.wikipedia.org/wiki/Absolute_zero#Negative_temperatures Mar 31 '15 at 11:56
• I want to point out that you wrote in your question "reduce to 0K asymptotically". One of the most fundamental properties of something that is asymptotic is that it never actually reaches the asymptote. That right there should tell you it never reaches 0K
– Jim
Mar 31 '15 at 18:02

In practice, no. In theory, also no.

The Universe is filled with photons with an energy distribution corresponding to $$2.73\,\mathrm{K}$$, called the cosmic microwave background (CMB). Every $$\mathrm{cm}^3$$ of space holds around 400 of them, so each second one $$\mathrm{cm}^2$$ is hit by roughly one hundred billion of these photons. That means that if you place your "stable body" in an ever-so-isolated box, the box itself will never come below $$2.73\,\mathrm{K}$$, and neither will the body inside. It will asymptotically go towards thermal equilibrium at $$T = 2.73\,\mathrm{K}$$.

Even if you magically removed everything else in the Universe but the body$$^\dagger$$, $$0\,\mathrm{K}$$ can never be reached. The reason is that this would imply zero motion of the atoms of the body, which is forbidden by law.

In practice, it is actually possible to have temperatures lower than the 2.73 K of the CMB. When a gas expands, it cools, and if it expands faster than it can be heated by the CMB, it can temporarily reach lower temperatures. This is the case for the Boomerang Nebula, which has a temperature of 1 K. The nebula will probably be heated to the temperature of the CMB in around 10,000 years or so.

$$^\dagger$$Or waited billions of years for the CMB to cool.

• Spot on. I like the first line in particular! Mar 31 '15 at 12:09
• Two comments: my understanding of the CMB is that it is still cooling itself, on cosmological time-scales, so that temperature is not necessarily stable. In addition, "it is possible to have temperatures lower than 2.73 K...": we also have refrigerators cooler than this, so clearly :) Mar 31 '15 at 12:55
• @zeldredge: You're absolutely right. 1) Yes, the CMB cools proportionally to the expansion of the Universe, so it will itself asymptotically go toward zero. Of course it will never actually reach zero, but if you are willing to wait, you can come arbitrarily close to zero. 2) Yes, we can artificially cool a system to very low temperatures (the current record is 1e-10 K, I think), but again it can never reach zero, and also this is not simply by letting the object cool.
– pela
Mar 31 '15 at 13:13
• This makes me wonder if in a hypothetical 0K voidverse, will that body at one point in time emit the last photon of blackbody radiation and then nothing anymore, despite being >0K? If yes, what temperature would it have... Mar 31 '15 at 15:55
• I think quantum effects (such as electron/positron pairs appearing out of nowhere) would prevent a true vacuum from occuring.
– k_g
Mar 31 '15 at 18:48

It´s impossible to drop a body temperature to absolute 0K. You must notice that, at the same time the body is radiating energy from its own temperature, it is also receiving temperature from other sources (regardless the distance of the source) like distant stars.