# Freezing a gallon of water

1. Mar 15, 2007

### Taiki_Kazuma

I have a Gallon of water at room temperature at Sea Level.
I want that gallon completely frozen in 5 seconds.

Supposing you don't account for impurities (ie. it's pure water)...

1) Is this possible?
2) How cold would it have to be?

Let's say you add 50% salt...

1) Is this possible?
2) Howcold would it have to be?

Also...how long would it take to be completely freeze if we were at the freezing point.

Also...what equations are being used? I've been out of School for a bit...but I want to know.
Thanks

2. Mar 15, 2007

### Staff: Mentor

This is such a vague question, that the answers are:

1. Yes.
2. Depends on how you do it.

1. Yes.
2. Depends on how you do it.

This snowmaker, for example, freezes ten gallons every five seconds: http://www.hedco.com/ [Broken]

Last edited by a moderator: May 2, 2017
3. Mar 16, 2007

### Taiki_Kazuma

That snow maker is taking something that is around freezing anyways and freezing it from what it looks like.

I want the minimal temperature to freeze 1 gallon of pure water from room temperature in 5 seconds.

There is a number for that. What I'm thinking that needs to be done for this problem has something to do with enthalpy. (i think.)
Basically I was thinking of figuring how much energy needs to be added to the system to decrease it to freezing, then how much energy needs to be added to freeze the system. Add the two energies together. Convert Work into time.

I just don't have any equations. My one Chem book from college...is well...I returned it. I just don't know where to begin. There has to be an exact number for this to occur in a timely manner. I'm pretty sure I accounted for all the variables in the system:

Time = 5 seconds
Pressure = 1 atm
Current Temperature = Room Temperature (98 F ~ is that room temp?)
Freezing Point = 0 C
Temperature Outside = ? ~ this is what we are solving for

To solve for temperature outside I believe we need:

Energy needed for the system to freeze....Beyond this my knowledge is cloudy.

I need equations...

I just noticed the previous reply stated this is vague...How can I make this concrete?

I want to basically instantly freeze something...How cold would the surrounding area be for this to happen?

wind chill is not a factor...It's a closed system. What variables am I not thinking of?

(Note: This is not actual homework. This is the search for personal knowledge. I'm curious and want to know how to figure this out.)

Last edited: Mar 16, 2007
4. Mar 16, 2007

### eaboujaoudeh

since its not a homework : u should apply Q = m c deltaT
Q is the heat needed, m is the mass of material, c 4.182 Kj/Kg for pure water, deltaT is your temperature differential..this is the amount ur looking for. physically its possible, but how to do it,well good luck

5. Mar 16, 2007

### Taiki_Kazuma

Ok...I'm a little rusty since I've been out of school for awhile.

M would be the mass of 1 gallon of water...which I'm pretty should I can figure out by googling it.

C...thanks for the constant ^_^

DeltaT is what I'm trying to find....

What's Q? How do I figure this out?

The problem with this equation...is I don't see how time is a factor. How do I specify...I want this to happen in 5 seconds?

-----

Unless... I'm actually suppose to be solving for Q. In which case the initial equation will give the ........ok I thought I had something. I'm lost once again ;-;

I thought that maybe delatT would be room temp minus freezing point. But I don't know how that works. Is Q's unit in Joules?

------------------

Ok I think I have it:

I need 1 more equation.
An equation that states how much "heat" or energy is needed to freeze a system in 5 seconds.

There needs to be an equation with Q and time in it.

What would this equation be?
Once I have that I can solve the problem.....ooooo I'm soooo close ^___^

Last edited: Mar 16, 2007
6. Mar 16, 2007

### eaboujaoudeh

yes Q is in Joules, if u divide by the time in the right side of the equation , u get Q in Watts, or J/s
translation would be : from T1 to T2 over a certain amount of time needs this much watts
to get m is simple : density x volume

7. Mar 16, 2007

### Taiki_Kazuma

Ok, How do I figure out how much energy is needed for the system?

Energy is Joules...which doesn't matter for time.

Watts would be the amount of energy per time.

So I need x amount of energy divided by 5 seconds will equal how cold it would need to be.

I have 2 variables from what I see.

Q and deltaT

I know one of the temperatures which is room temperature.
But I'm kinda at a lost of where to begin for Q.

Will I have to solve the energy required to take the gallon to freezing....and then how long it will take to completely freeze?
I'm thinking that's my next step.

I think I need 2 equations.

the first one to solve for Q.
In this equation would Surface Area be a factor? Or is Volume a factor?

================

Actually I think I might be going about this wrong. Should I first solve the equation for Q? Knowing that the deltaT will be Room temp minus freezing? Then solve it for temp? @_@

-----------------

http://www.svgs.k12.va.us/Courses/Physics/documents/GRR2_Chap14.pdf [Broken]

That pdf mentions something about latent heat. How do I find out the Q for that latent heat? If I found that and added it to the previous energy..wouldn't that be the energy to instantly jump it to the solid phase?

OH MY what's Q = m L?????????
(also in the same pdf) should I use that? o.o

Last edited by a moderator: May 2, 2017
8. Mar 16, 2007

### eaboujaoudeh

mass is the factor, neither surface area nor volume (well volume through mass anyway). deltaT is the difference of temperature !! its room temperature minus the temperature ur planning to reach which is zero or the freezing temperature. then after that u need to solve how much energy needed to freeze the mass u have, all that in 5 mins. i forgot how to calculate the freezing Q after we get to the freezing temperature line, mayb if u look it on the net i'm sure u'll find it

9. Mar 16, 2007

### Taiki_Kazuma

Thank you for directing me to the internet.....that's what I've been doing =P

* What are the states (or phases) of matter?

* What can cause a change in the state of matter?

During a phase change (e.g. ice melting) the temperature of the object will be constant even though energy is entering or leaving the object. The equation Q = m c D T cannot be used if the D T range includes a phase change. e.g. water T1 = 20o C T2 = -5o C.

The energy required to change the phase of a substance is called the latent heat. The latent heat of fusion refers to the energy per kg required to melt or freeze a substance. The latent heat of fusion for water is 3.33 x 105 J/kg or 79.7 kcal/kg. The latent heat of vaporization refers to the energy per kg required to vaporize or condense a substance. The latent heat of vaporization for water at 100o C is 22.6 x 105 J/kg or 539 kcal/kg. Table 14.3 gives values for the latent heat, L. Q = mL

Ok I found Laten Heat...as you can see. This is how you solve for that energy.

My problem is now....after reading that. How do I combine the two equations. I'm trying to change the phase of something. Which means I need to include that. Is this saying that no matter how cold it is outside, the water will freeze at a constant rate?

I know that I can add the 2 energies together which will give me the Q total.
After that...how do I figure the temperature needed to freeze in 5 seconds? I'm not understanding how you can just snap your fingers and say there it's now the temperature needed. What is that equation?

If you have been given me the answer to my question...can you please rephrase it. I'm not understanding and I would like to understand. Thank you so very much for your help thus far. I've gotten farther than I would have without you.

Last edited by a moderator: Apr 22, 2017
10. Mar 16, 2007

### eaboujaoudeh

ok the only way u can go on by this is to add the 2 Q's. then u divide them by the time period u want, and u get the value in kW. the reason we look for the kW value in engineering domains is because in all heat applications we are given the power ratings in kW, like heaters, AC's, heat exchangers, radiators.... alll are rated in kW. so we search to find the kW value of our need then we look at what device gives us the amount we are looking for. hope its clear enough..but that's how i understood ur final question

11. Mar 16, 2007

### Taiki_Kazuma

Ok...Let me try solving for kW so we have a number to work with. Then we'll go from there. It'll probably take me a few minutes. I will have a reply before 15 mintues are up from this time. Thank you so far for your help.

12. Mar 16, 2007

### eaboujaoudeh

ur welcome..but i have to go,,i'll reply to u as soon as possible. c you around

13. Mar 16, 2007

### Taiki_Kazuma

Based off of this
Density of pure water at room temperature (saying room temperature equals 25 C) is 997.07 g/L

3.79 L = 1 Gallon

m = D/V = (997.07 g/L) * (3.79 L) * (1 kg / 1000 g) = 3.78 kg

c = 4.182 KJ / Kg

DelT = T2 - T1 = 0 C - 25 C = -25 C

Q1 = m (c) delT = (3.78 kg) (4.182 kJ/ Kg) (-25 C) = -395 KJ*C ???

-----

L = 3.33 x 10^5 J/kg * (1 KJ / 1000 J) = 3.33 x 10^3 KJ/Kg
m = 3.78 kg

Q2 = m (L) = 3.78 kg (3.33 x 10^3 KJ/KG) = 126 KJ

-----------

Q3 = Q1 + Q2 = |-395KJ???| + 126 KJ = 521 KJ???

How does my work look so far? I think Q1 is screwed up. I have temperature...and it didn't cancel out.

Last edited: Mar 16, 2007
14. Mar 16, 2007

### Taiki_Kazuma

----

http://www.engineeringtoolbox.com/water-thermal-properties-d_162.html

This states that rougly the specific heat (I think that's what C is) for the range we are working with is roughly 4.182 kJ/(kg*K)

4.182 KJ/(kg*K)

So let's resolve for Q1 again....

3.79 L = 1 Gallon

m = D/V = (997.07 g/L) * (3.79 L) * (1 kg / 1000 g) = 3.78 kg

c = 4.182 KJ / Kg

DelT = T2 - T1 = 0 C - 25 C = -25 C + 273 K = 248 K

Q1 = m (c) delT = (3.78 kg) (4.182 KJ/(kg*K)) (248 K) = 3920 KJ

-----

Q1 = 3920 KJ
Q2 = 126 KJ

Q3 = Q1 + Q2 = 3920 KJ + 126 KJ = 4046 KJ

-------------

Q3 = 4046 KJ
t = 5 seconds

kW = Q3/t = 4046 KJ / 5 s = 809 KJ/s = 809 kW

--------

Now if all of this is correct.
How to I find the temperature required to freeze a gallon of water in 5 seconds? starting from room temperature.

How long would it take for this gallon to freeze? or what equation would be used to figure that out?

Last edited: Mar 16, 2007
15. Mar 17, 2007

### chemisttree

At any temperature less than 0C, a thin sheet of 1 gallon of water will freeze much quicker than a sphere of the same volume.

You can see that your OP is missing key information.
Russ was right...

16. Mar 17, 2007

### eaboujaoudeh

no 1st trial was correct.. C is the same in Kelvins or Celsius, cause delta T in kelvin or celsius is the same: (sorry i forgot the degrees in C)
deltaT in celsius: 25-0 = 25
deltaT in Kelvin: (25+273)-(0+273) = 25...same
the first one wass correct

17. Mar 19, 2007

### Taiki_Kazuma

Ok, so the shape of the liquid matters....

Then let's say it's a cube of liquid. Not a gallon.

1 m^3 will be the size of liquid.
Now how do I figure the time frame? I want this to freeze in 5 seconds....so how cold would it need to be outside for a cube of water to freeze starting from 25 Celsuis?

what equation do I need now to find the time frame? That's what I wanted from the beginning =\

If you guys would have said the equation for time requires surface area...or volume...I would have added that information to it. =\

So now the problem has changed a little.

Now I'm trying to have a Meter Cube of water to freeze in 5 seconds starting from Room temperature at sea level. @_@

where do I go from here?...Let me change the first equation a little.

-------------------------

-------------------------

D = 997.07 g/L
V = 1 m^3 = 1 L

m = D/V = (997.07 g/L) * (1 L) * (1 kg / 1000 g) = 0.99707 kg

c = 4.182 KJ / Kg

DelT = T2 - T1 = 25 C - 0 C = 25 C = 25 K

Q1 = m (c) delT = (0.99707 kg) (4.182 kJ/ Kg*K) (25 K) = 104.2 KJ

-----

L = 3.33 x 10^5 J/kg * (1 KJ / 1000 J) = 3.33 x 10^3 KJ/Kg
m = 3.78 kg

Q2 = m (L) = 3.78 kg (3.33 x 10^3 KJ/KG) = 126 KJ

-----------

Q3 = Q1 + Q2 = 104.2KJ + 126 KJ = 230 KJ

Now how do I figure the time it will take to freeze this....or how do I figure the temperature I need to freeze this in 5 seconds?

Is there some other variable of this problem I'm missing?

Here's a different question.
Let's say you have a 2-dimensional graph.
Y-axis is amount of solid (0% on bottom, 100% on top)
X-axis is time (0 seconds on the left, up to infinity on the right)

We are going to graph the rate at which a mass freezes, would this graph look like a parabola?
If so...wouldn't there be an easier equation to figure out how fast something completely freezes or how cold it would be to freeze something....or how frozen it is at a certain time frame?

Please note this is not actually homework for a particular class. I just want to know this information to apply it to something else I'm doing.

Last edited: Mar 19, 2007
18. Mar 19, 2007

### eaboujaoudeh

well if it was a H.W they wouldn't have asked u the ambient temperature to freeze this because its another subject.
The Q u are finding is the Q needed to move the temperature from a certain temperature to another, in your case you are moving the object from 25 degrees to 0 degrees, the energy needed to do that is 230 KJ, if u need to do it in 5 seconods then Q = 230/5 = 46 kW.
Now to find how much the temperature is outside then u need a mechanical engineer to calculate the heat convection/conduction from the outside to the inside...a whole different complex subject.

19. Mar 20, 2007

### Taiki_Kazuma

GREAT! Everyone here has been a big help with the terms that I'm looking for and the equations =)

Ok I think I have it now =)

http://www.physics.ubc.ca/outreach/phys420/p420_04/kenneth/theory.htm [Broken]

Based off of that site I think I have my answer =) ^____^

http://www.physics.ubc.ca/outreach/phys420/p420_04/kenneth/images/equations/conduction.gif [Broken]

Q = 230 kJ
t = 5 s
k = 0.61 J/msK * (1 kJ/1000 J) = 0.00061 kJ/msK For water at 30 C...it's close enough to room temperature
A = 1 m^2
Th = 25 C = 298 K
Tc = ? C = ? K
d = 1 m

-((Qd) / (tkA)) + Th = Tc
Tc - 273 = Tc in Celsuis

-((230 kJ * 1 m) / (5 s * 0.00061 kJ/msK * 1 m^2)) + 298 K = Tc
-((230 kJ*m) / (0.00305 kJm/K)) + 298 K = Tc
-(75409.83606 K) + 298 K = Tc
-75111 K = Tc

Umm....isn't the coldest anything can get 0 Kelvin? ??
So then this isn't practical then...right?

----------

When solving the problem for time, with my coldest temperature being absolute 0...I got an answer of about 5 hours to freeze my liter cube of liquid. ... Does that sounds more realistic?

I thought that If I left a liter out in the cold over night. Let's say 8 hours, it would be completely frozen... It just sounds ... yeah. Sounds like it takes forever to change phases.

Last edited by a moderator: May 2, 2017
20. Mar 20, 2007

### eaboujaoudeh

wel u can say so. but ur considering that the temperature is that of the boundary of the water and not the air (which mayb considered to be that of air in some rare cases, for simplicity), if u want to find that of the air u have to consider air-water convection. 2. u have to pay attention to the area and d that u r considering, if u take the area to be the top of ur cube then d will be the distance to the bottom. 3. when u get the -ve answer it means its impossible to do it in 5 sec..