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So, what is that, the fourth time you've removed yourself from this conversation?
- My standpoint is that the speed of energy transfer is what we're focused on
No, it's what you're focused on.
- ignoring your condescending tone
Wow. Go back and read your own posts in this thread. You have been extremely condescending towards me.
- Right. it's a cute equation. Positively adorable.
Would you speak to your work peers or boss the way you have to me?
Here's a rundown of your total contribution here:
1. This problem is too difficult for me; I have a masters degree in engineering. (Where'd you get it, Ohio State?)
2. Ambient conditions matter. Like, on a humid day, spherical ice melts less, but on a dry day, square cubes will melt less. Or is it the other way around? You never enlightened us on that, you only said that it mattered...
3. Spherical ice cools faster because it's bigger. (Highlighting to me that you don't understand the difference between shape and size.)
4. The laws of thermodynamics are over-simplifications of the real world and do not apply to something as complex as melting ice. (Even though those laws were conceived and proven by observations from the real world.)
Thanks for all your thoughtful contributions!
- You keep holding on to this as if wishing would make it true:
It does. It really does. All the stuff you're discounting is the difference between "real world performance" and "ideal performance" and even "ideal performance" doesn't get anywhere without conduction and convection at a bare minimum.
It doesn’t matter how you cool it, the answer is always the same.
Right there. You said it really does matter how you cool it. "The answer" being Q in the equation right before the quote of mine you used. "Q" stands for heat energy removed, which you said can be different depending on how you cool the 100g of whiskey from 21C to 15C.
- It would do no such thing.
That's exactly what I said.
- You're presuming the glass and atmosphere are perfect insulators
No, I simply know that heat flux doesn't go from cool bodies to warmer ones. Heat goes from warm to cool (glass to liquid.) That's one of the laws (2nd, I believe.)
- So, knowing that all of that heat energy went into the ice,
You know no such thing.
Yes, I do. If the ice didn't make the whiskey colder, what did? The warm glass, the warm air, or the warm hand holding the glass? 2nd law, bro.
It's clear to me that you're not going to wrap your head around this problem or how it's solved. I was hoping to get the light bulb to come on for you. You still want to calculate how long the cooling will take. (You and I seem to be in agreement that the spherical ice will cool the whiskey more slowly, so I'm confounded that you think you need to calculate exactly how much slower it is. For me, "well, it's ain't gonna cool faster, that's for damn sure!" is good enough.) I'm calculating how much ice will melt once the whiskey has reached the desired temperature. And as I've said before, the longer it takes, the more energy will have to be removed from the whiskey by the ice due to the heat transfer from the surrounding environment. Again, I don't even care for the precise answer, only "it sure as hell ain't gonna melt less" will do.
Ah, so you agree that the energy transfer doesn't differ. Good. You said earlier that it did, which had me confused.
So, yeah, at point in time t, when the fluid being cooled has experienced delta T, the amount of energy pulled from it is the same, regardless of how long it took to get to delta T. Good, that's what I was saying. The heat energy went into the ice, either warming it, melting it, or warming the melted water. We know it didn't go into the glass or atmosphere, that would violate one of the LAWS of thermodynamics.
So, knowing that all of that heat energy went into the ice, all we have to do is decide how it was distributed. If any of the solid ice remain un-heated (from -10 to 0C), then the balance of the energy must have been removed by phase change or heating the water.
So, does one large sphere warm more evenly than 4 small cubes? I don't need a precise answer, just >, <, or =. Or is it sometimes yes, sometimes no, depending???
It's not wrong. There is a change in energy taking place; the corresponding change in temperature for each body is governed by that formula. Your inability to understand that is why you can't solve this problem.
The amount of energy it takes to raise or lower a gram of water by 1C doesn't change depending on how you do it. It takes 1 calorie, period. It doesn't matter whether you are using natural gas, electricity, cold air in the freezer, or contact with another body. You saying that it matters doesn't make it true. Find a credible source that says otherwise and show me.
A few constants, pulled from the Internet (these are in Joules per gram per degree Kelvin, same magnitude as Celsius):
Specific heat capacity, ice: 2.108 J/g-K
Specific heat capacity, water: 4.20 J/g-K
Specific heat capacity, whiskey: 3.40 J/g-K
Latent heat of melting, ice: 334 J/g
Density of ice: 0.9167 g/cm3
The specific heat of water actually changes a bit with temperature, but not from one glass of water to the next. http://www.engineeringtoolbox.com/water-thermal-properties-d... So If we start with a fluid (whiskey) sitting in a glass (jar?) at room temperature. The whiskey, glass, and air around it are all the same temperature, so there is no net heat energy going into or out of the system. Let’s start with 100 grams of whiskey at 21C. If we then add a lump of ice to it and swirl it around, at some point in time the temperature of that whiskey, the original 100grams of whiskey, will be at an even 15 deg C. At that moment in time, a fixed amount of heat energy must have been removed from the fluid. That amount of energy is calculated with this formula:
Q = cp m dT
Q = (3.4J/g-K) (100g) (21C – 15C)
Q = 2040 J
It doesn’t matter how you cool it, the answer is always the same. You could blow cold air over it, put it in a plastic bag and drop it in the snow, or whatever. In all cases, if you want to get those molecules of whiskey cooled down by 6 degrees, you need to remove exactly 2040 J of energy from them. Any less, and it’s warmer, and more and it’s colder.
In our ice lump case, there is only one way we are comparing removal of that heat energy – by the ice we’ll put it in contact with. Some energy may come from the warming of the ice, some may come from the melting of the ice, and some fraction may come from the melted ice (water) warming up to the same temperature as the whiskey.
If the goal is minimal ice meltage, we would want to design our ice lump to warm up evenly. With 100 grams of ice to work with, and a starting temperature of -10C, it would be possible to cool this measure of whiskey by 6 degrees without even melting any:
Q = (2.108) (100g) (10C) = 2108 J
More than what is needed to cool the whiskey by six degrees, so it’s possible to design an ice lump to cool it without melting. Basically we’d want a lot of surface area and no thick parts to insulate bits of ice – basically every frozen molecule will need to pull their weight in order to cool the whiskey without any of their frozen colleagues melting.
The amount of energy that has to be removed from the whiskey in order to cool to a lower (drinking) temperature of, say, 10C, is:
Q = (3.4J/g-K) (100g) (21C – 10C) = 3740 J
So, now it’s not possible for 100g of ice to cool without melting at least a little. We can calculate the bare minimum of melting (let w = amount of ice melted, in grams):
3740 = (2.108) (100g) (10C) + (w) (344 J/g) + (w) (4.2) (10 - 0)
W = 4.4 grams
This is the minimum amount of ice that has to be melted in order to cool 100g of whiskey from 21C to 10C (using the starting ice lump of 100g at -10C.) If any of the ice in our lump doesn’t warm up to 0C, then some other portion of our lump will have to melt in order to remove that additional energy from the whiskey.
So, design-wise, if any ice is insulated from the whiskey (by being surrounded by more ice) it will not be effective at cooling, and the ice which is at the boundary condition will have to melt.
100g of ice will have a volume of 109.087 cm3. As a sphere, it will have a radius of 29.64mm, giving it a surface area of 110.4 cm2. Compare this to 4 cubes of 250g each – 30.1mm to each side, 217.4 cm2 of surface area – nearly double. This means that the 4 cubes of ice will be able to cool the whiskey nearly twice as fast as the sphere.
Furthermore, the ice at the center of the sphere has nearly twice as much insulation as the ice at the center of the cubes. Because the ice cubes warm more evenly than the sphere, there will be less melting as the fluid passes temperature T (10C).
If we then also consider the time factor, we see the case for the sphere getting even worse. Because it will take longer for the sphere to cool the whiskey, there will be more time for heat to transfer into the whiskey via the warm glass, the warm air, and your warm hand (on the glass). The rate of heat transfer is a function of delta T for each of these boundary conditions. The total heat energy transferred is directly proportional to the time. The longer the spherical ice takes to cool the liquid, the more the liquid will heat up from outside conditions, the more it will have to melt in order to cool to the given temperature.
Spherical ice is the worst possible shape in terms of its ability to cool a drink and not melt into it.
Well, first of all, I do respect your authority on this subject, and I do appreciate you taking the time to teach me/us something about it. That's why I wanted to engage on this subject in the first place.
At the risk of infuriating you, let me just seek/make clarification on these points:
- T1 to T2 will be faster for the ball, not slower. It will be faster through sheer volume.
Are you saying it's cooling faster because the ball is bigger? If so, how would a bigger cube cool in comparison? Or, more precisely, a cube of the same size (mass) as the sphere? Or do you mean the distance of the surface of the sphere to the center where T3 is? If so, isn't the distance from the surface to the center of the cube sometimes further (depending on the surface point)?
2. I never said that the rate of cooling for spheres vs cubes should be the same. In fact, from the very beginning I've asserted that
- obviously the ice with more surface area will cool faster than a sphere
The graph in your response shows that, yet you are insisting that I'm wrong. That chart does not show how much of the ice has melted, which is the key question I had posed.
Yes, I understand what you're saying, and I think I see where our understanding of the problem posed is different. I do appreciate everything you're saying, as you are clearly the right person to consult on this.
I believe that you are looking to model the entire response of the melting ice. As in, at time t1, the state of melt is X, at time t2 the state of melt is Y, etc. A full set of curves for temperature and amount of ice melted at any given time. A difficult problem to solve, for sure - I would use a computer model to solve this one.
My approach is different. I'm just trying to show that the amount of ice melted taking fluid from T1 down to T2 will be the same regardless of the shape of the ice. The time that it takes to get from T1 to T2 will be longer for the ball than the cube, so one could claim that "the ball of ice melts slower" - which is true, but the amount of ice that has melted by the time the temperature reaches T2 (the drinking temperature) will be the same. Furthermore, the rate of melting once the liquid has reached the melting temperature of ice (~0C) will be the same for either shape of ice.
And as far as me saying "all else being equal" that's how you address a given claim. I'm not wishing it so, I'm setting it as the parameters of the problem so I can address the claim of "it melts less because it has less surface area." It's not my claim. And there's no point in comparing A to B if you're going to have a bunch of other factors that are different. If the admen said "it melts less because it's only half in the drink," I'd have set up a problem around that claim. (But since I'm challenging shape, I might want to compare a sphere half in compared to a cube half in.)
As for the formula being the correct one, it is. I learned it in my high school Chem 1 class my freshman year, and it is still used today. In fact, you'll notice the same formula in the Enthalpy of Fusion wiki link.
In fairness, yeah, one could argue that all those Newtonian physics formulas are dead wrong over-simplifications now that one has taken a relativity course, but for validating a claim that there is a difference in A to B it should be a perceivable difference. The small stone and large stone dropped off a tower may not accelerate at exactly 9.8m/s/s and may not hit at exactly the same time, but most people would agree it's close enough; the small stone does not fall faster.
Well, you're point 1) is spot on. Steady state would be back to room temperature. What I meant was the state that the liquid and the solid are the same temperature, while the ice is melting. A graph of the liquid temp would be a slope down, then a flat line, then a gradual return to room temp. By steady state I meant the flat line of constant temperature (0C if at STP).
Points 2) ... all moot. Ice shape A vs ice shape B - all else being equal. Remember the ice is submerged in the drink. And if the sphere is not, you pointed out yourself that it would loose heat (melt) even faster. I was only trying to prove that it doesn't melt less.
So, two identical glasses, both containing a cylindrical-shaped water-alcohol mix of the same ratio, both cooled to the same temperature, both in the same ambient conditions. However complex the system is, I think it's fair to say that the two cylinders of fluid at the boundary conditions will absorb heat at the same rate.
q = m·ΔHf
Is that formula wrong because it doesn't contain a shape factor? Does the energy to melt one gram of ice differ based on the shape of the ice? (That's rhetorical, I know it does not.) Are the boundary conditions of 0C water/alcohol/ice somehow different? Maybe only in how much solid to solid contact we have between ice and glass..
Back when I was a young automotive engineer at a tier-1 supplier, I had a mentor tell me "always do what's best for the program - no one will ever fault you for that." In the broad sense, what he meant was "do what's best for the car, not what's best for the company you work for, nor the customer(OEM), nor yourself."
That advice has served me well over the years, mostly because it's fully defensible and doesn't participate in the zero-sum game of screwing the customer / screwing the supplier. (I later worked for an OEM.)
There aren't really any famous engineers, anyway. Maybe a few designers are famous within the industry, but that's rare.
OK, after doing a bit more web surfing I basically found somebody that's done this problem already, calculating for ice vs stones.
Again, note there is no place in the formula to consider shape. He does not calculate the rate of change, either, but it should be clear that spherical shape is the slowest possible (least surface area for heat exchange.)
I wouldn't have a problem with it if the admen were saying "buy these ice sphere makers because they look slick." It's because they saying something that is factually inaccurate, and consumers at large are being deceived and ultimately dumbed-down as a result.
This is just one example; I see this kind of thing all the time. It usually starts with one bit that is true, establishing credibility, then followed by one or more fallacies: "Spheres have less surface area than cubes..." True. "...and are therefore cools your drink faster with less melting!" False and false.
Bah! excuse me I need to go chase some kids off my lawn..