Who Loves Math!

[JewishIntent]

Ok this is definatly a bit more chem than math, but since chem is math . . .

Anyways, I am lookin to do some minor experiments at home this weekend and the only thing i still need is an equation for heat dispertion. I'm not sure what the exact theory/equation is called so its very hard to just google for it.

What i need is the equation that dictates the results of the following circumstance.

How long will it take for X-amounts of a liquid at T-temperature to drop below 32 degrees f when put into a freezer with an ambient temp of C.

I do remember from way back in chem that these types of equations have many factors such as atmospheric density and the such, but i am just going to null those since i don't need to be that painstakenly accurate in my calculations.

Any help would be awesome.

Edit: i should probably add the liquid in question is water. that will probably affect the equation.

[morganlefay]

Maybe you just dont know how to google

http://www.google.ca/search?hl=en&ne...G=Search&meta=

MLF

[JewishIntent]

Well all of those site have equations that are a bit beyond what i need, but thanks for the try. I was hoping to get the answer here, but it looks like i may actually have to hit the school library and browse some chem books. . . . .

[Nokia]

Maybe google for a science forum then?

[unhappy]

it's called physics ... not chem


get your sciences straight

[JewishIntent]

unhappy: hmmmmm . . . well i guess you are right. I was thinking more of it as the physics of chemistry since i am going to be using this equation to seperate water from various liquids which have a freezeing temp lower than that of water.

Nokia: i will defanitly try finding a forum to post this on, not sure why i didn't think of that, probably because the sheer volume of collective knowledge here at AO dwarfs that of many if not all other forums.

[sec_ware]

Hi


Given:
- Heat reservoir "freezer" at temperature: C
- Liquid is initially at temperature: T_0
- Surface of the liquid: A
- Mass of liquid: m
- specific heat of the liquid: c

- surface heat conduction coefficient: h


We want:
- How long does it take such that the liquid is at temperature
T_1=32 deg f = 273.15 kelvin K


Assumptions/Simplifications:
- The liquid is cooling down via convection and radiation
within the freezer, where I assume that the temperature
inside the freezer remains constant ("heat bath"). From a
"kinetic theory"- point of view, this is not true, but sufficient
here.
- the surface of the liquid remains constant (...)
- ...

Solution:

Newton's law of cooling[1] tells us that within the fridge
(Q is heat quantity, t is time, T is the current temperature of the liquid)

dQ/dt = h A (T - C)

It can be shown (using dQ = -m c dT and integrating Newton's law)
that the temperature at a given time t is

T= C + (T_0-C) exp( -h A t/mc)

Solve for t:
t= -log[(T-C)/(T_0-C)] * m c / (h A)

and insert T=T_1.

Hope, I did not misunderstand you...

Cheers

/edit: I forgot the mention a little, but interesting detail: how long
would it take to reach equilibrium, ie the liquid is as cool as the freezer.
Answer: infinitely long. This is the danger of simplified models.


[1] http://en.wikipedia.org/wiki/Heat_conduction (bottom)

[JewishIntent]

In case anyone was wondering what i found regarding this question:

I posted my scenario on a chemistry forum, and unhappy it was confirmed that this is a chem not physics question. I was basically informed that for a real life scenario such as mine the best and fastest way to figure the time out is through trial and error. There are way too may variables such as viscocity, viscocity over time, surface area, cup thickness, material, heat coefficients, freezer area, placment of freon coils, and the list goes on.

Thanks again for contributing what you guys could. As always the members of AO continue to impress and facinate me with the wide range of knowledge you all posses.

[The Grunt]

Equation would be mass x Specific heat x temp change = mass x specific heat x temp change

[sec_ware]

Hi

Take this with some sense of humour ...
I am wondering what people participating in a physics forum would say,
whether this is chemistry or physics ...

One should not always believe what people say in forums (even if the
same wrong arguments are repeated endlessy). JewishIntent
this is a physics question:
All processes, which leave the involved substances unchanged,
are assigned to physics. Thermodynamics, as we are dealing
with here, is physics. Chemical reactions, which change the bindings
between atoms, modify the substance. But then phase transitions,
such as liguid-gas, are physics....
Well, this is a forum - can you believe me?


I am wondering. Let me make a simple prediction using a specific
experiment:
- take 1kg soup at 60 deg celsius (140 deg fahrenheit, 333.15 K)
in a very thin cubic box (closed, metallic is preferred).
- put the soup in a freezer at -20 deg celsius (-4 deg fahrenheit, 253.15 K).

How long does it take until the soup has reached 0 deg celsius (32 deg fahrenheit, 273.15 K)?
(neglecting freezing of the soup)

Prediction: (all complicated properties of the soup are collected in the
substance properties c and h).

m=1kg
A=0.06 m^2
c=4182 J/(kg K) (maybe a little more or less. this is the water value).
h=77'000'000 W/(m^2 K)
--> m c / (h A) =0.0009/s

It will take about 1540 seconds or 26min to cool down 1 kg of soup
(in a metallic closed cubic box) from 60 deg celsius to 0 deg celsius
in an environment of -20 deg celsius.
A crude approximation of course, but at least a value.

for a real life scenario such as mine the best and fastest way to figure the time out is through trial and error

They are right. By experiment you will get values for the constant h and c, or
more simplified for the ratio "m c / (h A) ". Then you have the fundamental
quantities to perform predictions for further experiments


Cheers