Hi James,

I see what you are saying, but (looking at the diagram):

 |   |      |   |
 |---|------|---|
 |   |  b   |   |
 | a | milk |   | 
 |   |______|   |
 |              |
 |    water     |
 |______________|
  ^^^^^^^^^^^^^^ <- heat from stove

I don't understand what you're trying to explain to me, there is a
disconnection between the two of us somewhere.

1) How can I heat b to x degrees above a, if I can't directly heat b?
not only because direct heat from the stove would make the bottom of b's
pan a hot spot, but I also can't use a heater immersed in b because as
the milk curdles and can't be stirred, the heater itself would become a
hot spot, no?
2) If a < x = b, even applying heat to a, wouldn't b start to cool until
a = x = b and only then start to heat up again as a become hotter than
b?

With the previous option 1, if a = 90 and b = 90, we're ok, then I
slowly increase a to 91 and keep it there until b = 91, at which point I
then slowly increase a again to 92 and keep it there until b = 92 and so
on, until they're both at 100.  I don't see how the 1F/min rule would be
violated if I increase a at 0.5F/min.

Thanks.


-Mario



-----Original Message-----
From: piclist-bounces@mit.edu [mailto:piclist-bounces@mit.edu] On Behalf
Of James Newtons Massmind
Sent: Thursday, January 12, 2006 2:24 PM
To: 'Microcontroller discussion list - Public.'
Subject: RE: [OT] Need help with some thermodynamics concepts (or source
of it)


> 6. over the period of 30 minutes raise the temperature of the milk to 
> 100F, and never raise more than 1F/minute.

Again, method 1 or 2 will violate this rule. As I said before you need
to use a third method:

3) heat b to a temperature that is x degrees above a and keep increasing
b until a hits the target then remove b. This one will give you a
straight line temperature increase which will make it easy for you to
predict when the target will be reached and adjust x accordingly on the
fly. "A" WILL reach the target temp, and will probably overshoot it
slightly unless you can remove b instantly.

You can avoid the overshoot by not increasing the temperature of b past
the target temperature so that it curves off like 1) as it approaches
the target.

I have some (minor) experience with this and I know if you try to go
from 90 to 100 by floating the curd pan in 100 water, the initial
temperature change in the curd will exceed 1' per minute.

As the curd can't be mixed, you must keep it fairly thin and measure its
temperature from about half way between the center and the outside edge.

---
James.
 


> -----Original Message-----
> From: piclist-bounces@mit.edu
> [mailto:piclist-bounces@mit.edu] On Behalf Of James Newtons Massmind
> Sent: 2006 Jan 11, Wed 15:54
> To: 'Microcontroller discussion list - Public.'
> Subject: RE: [OT] Need help with some thermodynamics concepts 
> (or source of it)
> 
> > 1) heat a to the temperature I want b to be heated up to
> and then keep
> > a constant there until b reaches the same temperature
> 
> I don't see why you need any calculations... This option will
> bring b up to temp at a rate dependant on the mass of b and 
> the insulation between the two assuming they are both mixed 
> to uniform temperature inside. The temp graph in b will be a 
> curve which will flatten out as b approaches the target 
> temperature. It will never /actually/ reach the target but 
> will come very close.
> 
> > 2) heat b to a higher temperature than I want b to be at
> and then let
> > it cool down while b heats up with the heat given off by a until
> > eventually both reach the same temperature
> 
> We assume this should have started with "heat /a/ to a higher..."
> 
> This one depends on the ratio of masses between a and b and
> the insulation... And the mixing...  The curve will be 
> steeper at first and then flatten out again. Same problems.
> 
> 3) heat b to a temperature that is x degrees above a and keep
> increasing b until a hits the target then remove b. This one 
> will give you a straight line temperature increase which will 
> make it easy for you to predict when the target will be 
> reached and adjust x accordingly on the fly. "A" WILL reach 
> the target temp, and will probably overshoot it slightly 
> unless you can remove b instantly.
> 
> Feedback removes variables.
> 
> ---
> James.
>  
> 
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