Re: ATM BVC Weirdness part II

[Aplanatic@aol.com]

I wrote:

<<As you might recall, the thermal diffusion time constant goes like the length scale squared.  Thus, it thermalizes quickly through its thickness but very, very slowly across its diameter.  A two inch thick Pyrex mirror has a thermal time constant of about 15 minutes in the thickness direction, but a time constant of many hours across its diameter. >>

Mike replied:

<<How exactly does this work? I've been sitting here, scratching me head, and can't get it. How can a mirror have two different thermal time constants? Is this to say that the expansion and contraction has a significant time lag after thermal equialization, that is to say that the mirror is at ambient temp, yet still at a non equalibrium state of expansion?  >>

Sorry for the confusion, Mike.  A rod of Pyrex 2 inches long will take 4 times as long to thermally equilibrate than a rod 1 inch long, in other words, the time it takes to equilibrate goes as the square of the distance.  

Let's say that our mirror is 2" thick and 16" in diameter.  If there is a uniform temperature difference between the front and back of the mirror, it will take roughly 30 minutes to equilibrate.  If the temperature difference is between the edge and the center of the mirror, then it will take roughly 2 hours to equilibrate.  If the temperature difference is between one side of the mirror and the other side (across a diameter, say) then it will take roughly 8 hours to equilibrate.

All this is based on conduction through glass and does not take into account the effect of air.  A fan blowing on the mirror will dramatically lower the equilibration time.

Dave Rowe