Searching \ for '[OT] Need help with some thermodynamics concepts (' in subject line. ()
Help us get a faster server
FAQ page: www.piclist.com/techref/index.htm?key=need+help+with+thermodynamics
Search entire site for: 'Need help with some thermodynamics concepts ('.

Exact match. Not showing close matches.
'[OT] Need help with some thermodynamics concepts ('
2006\01\11@153158 by

I'm trying to find out where I can find the following information.  My
initial google searches have only led me to half the answer.  If you know
a good source of information on how to solve this I'd appreciate it if
you'd let me know.  Thanks.

I need to build an aparatus that will heat up a couple of gallons of water
[max].  But in this tank there will be another container with milk in it.
The milk cannot be heated directly otherwise the flavor of the end product
can be affected.

I think a little sketch will help me describe what I need help with.

___________
|    ___    |
| a |   |   |
|   | b |   |
|   |___|   |
|___________|

First, assume the b container is not in the picture, so, if a is at 0c and
I need to raise it to 30c in 30 minutes, then I'll need to raise the
temperature of a by 1 degree per minute.  Easy so far.

But, what I am trying to find out is the rate of change for a if b is at
15 and it needs to be at 30 in 30 minutes.  So b will need to heat up at
0.5 degree per minute, but what is the rate of change for a in order to
accomplish this?

Thanks.

-Mario
Mario Mendes Jr. wrote:
> But, what I am trying to find out is the rate of change for a if b is
> at 15 and it needs to be at 30 in 30 minutes.  So b will need to heat
> up at
> 0.5 degree per minute, but what is the rate of change for a in order
> to accomplish this?

That depends on the thermal insulation between A and B.  This will be hard
to calculate up front.  At best you can get a ballpark idea.  The only real
way to determine this is to build it and measure the result.  The flow and
amount of agitation in both liquids will also have a lot to do with it.

******************************************************************
Embed Inc, Littleton Massachusetts, (978) 742-9014.  #1 PIC
consultant in 2004 program year.  http://www.embedinc.com/products
What is the thermal resistance of the container around B? You've got an RC
circuit here where the thermal resistance of B's containter is R and the C
is the heat capacity of the fluid B. If the thermal resistance is low, or
the heat capacity is low, the temperatures of A and B might track pretty
closely, with B a little behind A. Also need to consider the RC formed by
the thermal resistance of A and the heat capacity of the containter of B.
This can get tricky since the heat transfer from A to B's container is by
convection instead of by conduction. MUCH more complicated!

Time for an experiement?

Harold

{Quote hidden}

> -
Well, I have done some more digging around on the internet and found a
bit of information, but nothing that leads me to find the holy grail for
my setup.  It seems that I have 2 options:

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
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

For whatever reason (maybe the wrong one) I think that the second
approach will be faster than the first, but also a lot harder to do
without some magic formula to get some ball park values to play with.

I am willing to experiment, as this should be quite fun to do just like
physics class in high school (I never got to go to college).  But before
I embark on a fun filled Saturday, are there any other ways to do this
(better or worse)?

Thanks.

-Mario

{Original Message removed}
> 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.

{Quote hidden}

In method 1, if you keep the outside fluid at the desired temperature, the
inside fluid would eventually reach that temperature. The amount of time
it takes is based on the thermal resistance of the container of the inside
material and the heat capacity of the inside fluid. You also have to
consider the heat capacity of the container around the inside fluid,
though this may be small compared to the heat capacity of the inside
fluid.

I'm assuming this double fluid method is so you don't have "hot spots" in
the inside fluid where the temperature is non-uniform due to hot spots on
its container. It seems this could be avoided by using a container that is
highly conductive (copper) and spreading a heater around it. A thin
plastic coating could protect the inner fluid from contamination from the
copper while having minimal thermal resistance.

Back on the two fluid approach, can you put a temperature sensor on the
inside fluid? If so, you can then tune a PID control loop to quickly get
the temperature where you want it to be without overshoot. Again...
experimentation!

Good luck!

BTW, my junior high science fair project was about heat capacity. I ran a
submersed electric heater of a known wattage for a certain number of
seconds and observed how much the water temperature increased. That was
something like 45 years ago...

Harold

--
FCC Rules Updated Daily at http://www.hallikainen.com
Thanks to all that replied to this.  Of special note was the observation
that the system behaves like an RC circuit.  Very nicely put, Harold.

After doing some research, which led me to finding out what a joule is
(and watt-hour, calories, erg, BTU, etc), I figured out that method 1
bellow is the best for my specific need. Explanation follows the
diagram:

|   |      |   |
|---|------|---|
|   |      |   |
|   | milk |   |
|   |______|   |
|              |
|    water     |
|______________|
^^^^^^^^^^^^^  <- heat

1) heat water to the temperature I want milk to reach and then keep
water's temperature constant until milk reaches the same temperature
2) heat water to a higher temperature than I want milk to heat and then
let it cool down while milk heats up with the heat given off by water
until eventually both reach the same temperature

For my purposes, it is important that the center of the milk reaches
temperature X without any of its mass going above X, and method 1 does
just that.  With method 2, if not carefully monitored and controlled,
the mass surrounding the center of milk can raise above X before the
center reaches X.  Therefore, for simplicity sake, method 1 is better.

Another complexity that I found during my research is that the specific
heat of the milk will change as time goes by because it will solidify
(will change from milk into cheese).  This also adds the small problem
of not being able to keep stirring the milk while it heats up as I can
do with the water to maximize the heat transfer.

Thanks again.

-Mario

>2) heat water to a higher temperature than I want milk to
>heat and then let it cool down while milk heats up with
>the heat given off by water until eventually both reach
>the same temperature
>
>For my purposes, it is important that the center of the
>milk reaches temperature X without any of its mass going
>above X, and method 1 does just that.  With method 2, if
>not carefully monitored and controlled, the mass surrounding
>the center of milk can raise above X before the center
>reaches X.  Therefore, for simplicity sake, method 1 is better.

This will depend on how much you stir the milk. It will certainly be a
problem if you do not stir it, but if you do not stir it then I suspect you
will find an unacceptably long heating time which may make the milk do other
funny things - such as curdle around the edges - while the centre of the
milk mass will still be only vaguely warm.

>Another complexity that I found during my research is that
>the specific heat of the milk will change as time goes by
>because it will solidify (will change from milk into cheese).
>This also adds the small problem of not being able to keep
>stirring the milk while it heats up as I can do with the
>water to maximize the heat transfer.

I am not up with the temperature and stir rate required to make cheese, but
it seems to me that if you stir it too vigorously then you will have cheese
anyway, whatever heating system you use. ;))

Mario Mendes wrote:

> Thanks to all that replied to this.  Of special note was the observation
> that the system behaves like an RC circuit.  Very nicely put, Harold.

Many systems can be put into a U/I/R/C/L analogy, just as other analogies
(water) often are used to describe the behavior of electrical circuits.
You'll find more information about thermal equivalents in some datasheets
and app notes for power semiconductors; sometimes they give the electrical
analogy of the thermal behavior of the chip in the case, to help with the
calculations of what happens thermally when driving the chip with short
pulses (as opposed to thermal equilibrium, which is what you use when you
make those W/K heat sink calculations).

> After doing some research, which led me to finding out what a joule is
> (and watt-hour, calories, erg, BTU, etc)

Stay with joules and watts -- makes your life a lot easier. There's no need
for different energy and power units.

{Quote hidden}

With method 2, if you heat /all/ the water (I assume the water is stirred)
to a temperature above X, the milk /will/ go above X at the borders. Maybe
only a little, but it will.

> Another complexity that I found during my research is that the specific
> heat of the milk will change as time goes by because it will solidify
> (will change from milk into cheese).  This also adds the small problem
> of not being able to keep stirring the milk while it heats up as I can
> do with the water to maximize the heat transfer.

Should've said you want to make cheese in the first place -- that's
different from heating milk. It's different in that it presumably takes
hours (?), therefore the longer time of method 1 may not be a problem.

If possible, you could think of stirring the milk during the heating phase,
to get up to temp quicker, and then just let it sit, with the water just
providing the necessary power to maintain the temp as the cheese thickens.

Gerhard

Well, since there still is some curiosity as to the heating of milk and
the cheese making process, let me do a quick overview of the process for
you.

Note:  it cannot be heated up on the stove directly, not only because the
hot spots can affect the taste but those also introduce other
inconsistencies such as color, smell, hardness/softness, etc.

1. pour milk into a pan
2. bring temperature to 90F
3. add [bacteria] culture starter, and keep it at 90F for 45 to 60 minutes
- this will "rippen" the milk by increasing it's ph and acidity, also
different bacteria is used for different type of cheeses
4. add diluted rennet and let it sit for 45 to 60 minutes, this will
curdle the milk and at the end you'll end up with a mass that resembles
tofu that has been heated in soup.
5. dice the curdle (cut into small pieces)
6. over the period of 30 minutes raise the temperature of the milk to
100F, and never raise more than 1F/minute.
7. It is cheese now, you can even eat it at this point. The remainder of
the instructions are different for every type of cheese that you make.

So, stiring the milk is ok in step 2, 3, but not after that.  The
temperature control is specially important in step 6 because movement will
cause the curdle to lose fat and protein which will affect the end result.
Note that all times and temperatures (except for step 2 and 3) will
differ depending on the type of cheese you're making.

While it can take up to 4 hours to go from milk to cheese, the total
amount of time you spend actually doing anything is about 1/2 hour.  But
during those 4 hours you're required to stick around checking temperatures
and making adjustments to the stove.  The initial crockpot topic got
thinking about automating the process a bit, which would allow me to step
away for a while and do other things while milk became cheese all by
itself.

First I thought of using aquarium heaters directly in the milk, but that
proved to be a bad idea considering the temperatures involved, so I moved
on to aquarium heaters in the water container, which was better, but now
depending on the heat transfer between the masses, maybe many aquarium
heaters would be needed to be controlled because of the amount of heat
necessary.  That is when I started wondering how I could calculate the
heat and the transfer rates, etc.

Thanks.

-Mario
> 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 removed}
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 removed}
Arrgh.... a <-> b Got the a and b reversed.

Heat a to x degrees above b...

What I understood you were going to do with method one was heat a to 100'
and let b catch up on its own. That won't work. How you described method 1
just now is basically what I was saying.

---
James.

> {Original Message removed}
Hahahahahhahahaha

I knew it!!  I knew there was some very small and simple disconnection
between the 2 of us.

Thanks.

-Mario

{Original Message removed}
I think the time constants associated with the heat-the-water,
transfer-to-the-milk scenario will get you. I think they use "flash plates"
in this kind of process wher the milk runs over the heated (cooled) plate at
a rate to change it to the desired temperature. The plate is a constant
temperature and the rate of flow is contolled to get the desired output
temperature.

Are you pasteurizing the milk? That is what it sounds like to me!

John Ferrell
http://DixieNC.US

Silly question: can you use a microwave oven ? The bugs are not affected
by the microwaves afaik, but this needs to be tried. Because if you can,
then you ca control the heating directly into a, and without stirring at
all. And controlling a magnetron on/off or proportionally is not that
hard. (proportional control actually works - try it - yes if will be off
frequency but the radiation stays in the box - output power is
proportional to effective anode voltage squared or raised to a higher
power).

Peter
I've tried it with a few different microwaves and it does not work well.
Even with the rotating platter the microwaves still produce hot spots
inside, so as the food spins, whatever parts pass through those hot
spots tend to heat a lot faster.

-Mario

{Original Message removed}
No, not pasteurizing it.  In fact the milk is bought at the store and is
already pasteurized.  One cannot get unpasteurized milk around here,
sadly, since it makes a much tastier cheese.

-Mario

{Original Message removed}
Mario Mendes <mario <at> mmendes.com> writes:

>
> I've tried it with a few different microwaves and it does not work well.
> Even with the rotating platter the microwaves still produce hot spots
> inside, so as the food spins, whatever parts pass through those hot
> spots tend to heat a lot faster.

Try again, but this time use a microwave 'stirrer' ? (A microwave stirrer is a
fan-like device made of metal that spins inside the oven and rapidly moves the
standing wave nodes inside - much faster than any spinning platform). Better
microwaves have such a stirrer (in addition to the rotating plate).

Peter

Love this list.  We learn to make cheese!

Something you said,

>Another complexity that I found during my research is that the specific
>heat of the milk will change as time goes by because it will solidify
>(will change from milk into cheese).

suggests that reactions inside the mixture will absorb or release heat as
they happen.  To incorporate this idea into your remark, I'd say that
nothing can just change its specific heat unless it changes into something
else, and that something else will have to give up the extra heat (or
absorb the needed heat).   Simple melting and freezing exhibit this,
too.  This will interfere with your predictions.

Though, I am guessing the effects are small, because no one has mentioned this.

Barry

More... (looser matching)
- Last day of these posts
- In 2006 , 2007 only
- Today
- New search...