# [time-nuts] Thermal Time Constant

Bruce Griffiths bruce.griffiths at xtra.co.nz
Wed Mar 10 00:15:21 UTC 2010

```Bruce Griffiths wrote:
> Brooke Clarke wrote:
>> Hi:
>>
>> For some time I've considered surrounding a free running 32678 Hz
>> oscillator (like a Dallas 32khz, or one of the newer Maxim units)
>> with thermal mass and insulation in order to get the time constant
>> into the range of some days.  To get a feel for it a simple
>> experiment shows that a half inch diameter brass rod 3.75" long (102
>> grams) has a thermal time constant of about 6 min 35 seconds when
>> wrapped lightly in a towel.
>>
>> Is there a way to calculate the amount of aluminum and Styrofoam
>> needed to get a time constant of say 100 hours?
>>
>> This came up in relation to WWVB clocks that free run for most of the
>> time.  When you compare WWVB clocks it's not uncommon to see tens of
>> seconds difference between them.  http://www.prc68.com/I/Loop.shtml#TC
>>
> withstand (determined by internal dissipation and acceptable
> temperature rise above ambient).
>
> If for example the dissipation is 10mW and acceptable temperature rise
> 10C then thermal resistance will be about 1000C/W.
>
> The thermal capacity required can then be calculated from the time
> constant:
>
> C= 3.6E5/1E3 = 360 J/C requires about 7.2 kg of aluminium.
>
> The required thickness of styrofoam can then be calculated from the
> surface area of the aluminium block.
>
> Achieving a thermal resistance of 1000C/W may be a little difficult
>
> Bruce
>
>
Oops, the specific heat of Alum9inium is about 0.2Cal/gm/C or 0.8371
J/gm/C so the mass of Aluminium required would be 430gm if the thermal
resistance to ambient were 1000K/W. With a thermal resistance of 100C/W
you need 4.3Kg of aluminium ....

Bruce

```