Can an object ever fully reach ambient temperature in an isolated environment?

[thetexan]

I left my unopened icy cold Coke out on my desk yesterday. When I came in today it had, of course, lost it's icy edge and had achieved room temperature.

Then I asked myself...will my drink ever actually achieve room temperature or will it always be slightly colder then room temperature?

Can something cold ever finally equalize to ambient temperature if there is nothing to keep it cold?

tex

 

[hilbert2]

The temperature difference between a cold object and the room temperature decreases exponentially with time (here we assume that the heat conduction in the drink is so fast that its temperature remains uniform during the warming up), so in principle it will never become zero. You can Google "Newton's law of heating/cooling" for more information. This is a bit similar to how radioactive decay happens with some half-life.

 

[hilbert2]

Yeah, Zeno's paradox... :)

 

[DrClaude]

The temperature difference between a cold object and the room temperature decreases exponentially with time (here we assume that the heat conduction in the drink is so fast that its temperature remains uniform during the warming up), so in principle it will never become zero.

That's a too idealistic picture. In reality, there are constant fluctuations in temperature (too small to measure, but they are still there), such that the object will reach room temperature within these fluctuations in a finite time.

Edit: In addition, Newton's law of cooling doesn't hold if the difference in temperature between two objects is of the order of these fluctuations.

 

[hilbert2]

That's a too idealistic picture. In reality, there are constant fluctuations in temperature (too small to measure, but they are still there), such that the object will reach room temperature within these fluctuations in a finite time.

Edit: In addition, Newton's law of cooling doesn't hold if the difference in temperature between two objects is of the order of these fluctuations.

I know that... Also, if one keeps observing radioactive decay of some sample, there will eventually be a time when every single nucleus has decayed, but if you put the sample in an isolated box (similar to what Schroedinger's cat is in) and start waiting without looking in the box, you will never reach a point when there is exactly zero probability for any undecayed nuclei to be left in there.

 

[DrClaude]

I know that... Also, if one keeps observing radioactive decay of some sample, there will eventually be a time when every single nucleus has decayed, but if you put the sample in an isolated box (similar to what Schroedinger's cat is in) and start waiting without looking in the box, you will never reach a point when there is exactly zero probability for any undecayed nuclei to be left in there.

We're considering classical physics, not QM. There will be a point where, even theoretically ("in an isolated box"), we can say that the temperature of the object is the same as that of the room, provided we take into account fluctuations.