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.
Still wrong. You're oversimplifying, as discussed. This is not a first law of thermodynamics problem it is a: - convection heat loss problem (ice to whiskey) - conduction heat loss problem (ice to whiskey) - laminar flow problem (convection caused by thermoclines within whiskey) Do you understand the difference between "accuracy" and "precision?" You have some very precise calculations going on there - numbers and equations and logic oh my - but you do not have any accuracy as to what you're calculating. Yes, in a completely magical closed system something would have to lose so many joules in order to cool so many kelvin. And then the real world stepped in and smashed your dreams. 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. I know that you only want to use the math that you understand, but the math you don't understand is why I'm going to keep telling you you're wrong. And once more with feeling: I wouldn't model this. Period. I'd test it, fit a curve to it and use the data empirically in the future. When you model a complex system with a simplification bad things happen.That amount of energy is calculated with this formula:
Q = cp m dT
It doesn’t matter how you cool it, the answer is always the same.
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.
No. But the SPEED does. The EFFICIENCY does. And your entire line of questioning is about "how long."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.
Find a credible source that says otherwise and show me.
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???No.
Show me where. But point in time t is variable and indeterminate, delta T is variable and indeterminate. THAT'S WHAT YOU'RE SOLVING FOR. It would do no such thing. You're presuming the glass and atmosphere are perfect insulators, which would violate the laws of thermodynamics. You know no such thing. …and how it got there. …and how long it took. …and what the efficiency was. …all of which are variable based on the geometry of your ice and the convection caused by it, which is - again - a variable you're attempting to solve for. wat Remember when I said I wouldn't model this with a ten foot pole? That statement has not changed veracity lo these many weeks.You said earlier that is 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
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?
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. That's exactly what I said. 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.) 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.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.
It would do no such thing.
You're presuming the glass and atmosphere are perfect insulators
So, knowing that all of that heat energy went into the ice,
What I said: What you said: What I said: So what you're saying is that I agreed with you when I quoted you to say you were incorrect. Just so we're clear: Your standpoint is that the amount of energy is the same, therefore nothing else needs to be calculated. My standpoint is that the speed of energy transfer is what we're focused on, therefore we have to calculate a whole bunch of ugly shit. Worse, you're no longer arguing fact, you're attempting to depose me - you're trying to argue my statements hold no value because you think you've tricked me into contradicting myself. This isn't court, this is physics, and no matter how much you wish to dance around the issue, I have a lot more training in it than you do - which means, I suspect, that you can't even follow my arguments closely enough to understand them. Further, it doesn't matter how much smarter you think you are or how incorrect you presume me to be, the fact remains: I spent several thousands of dollars being tested on this stuff in an ABET-certified 4-year institution (one of the top ten in the country at the time, in fact) and I feel like I'm beating a dead horse: This isn't a Physics 101 problem. Which only makes the following that much more insulting: So. You and your high school physics can be as self-assured as you wish about this particular problem. I said before and I'll say again: it's a lot more complex than you think. I'll add this, though: I no longer have any interest in helping to illuminate the problem to you. I've been purposefully ignoring your condescending tone in the face of an exceptional amount of patience, but I can't do it any more. Good luck with this and your future endeavors.Right there. You said it really does matter how you cool it.
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.
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.
No. But the SPEED does. The EFFICIENCY does. And your entire line of questioning is about "how long."
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.
So, what is that, the fourth time you've removed yourself from this conversation? No, it's what you're focused on. Wow. Go back and read your own posts in this thread. You have been extremely condescending towards me. 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!My standpoint is that the speed of energy transfer is what we're focused on
ignoring your condescending tone
Right. it's a cute equation. Positively adorable.