I went to school for Chemical Engineering, this is my time to shine! You got it in the bullet point. A closed system (your container) wants to reach thermal equilibrium. This is done by the warmer...
I went to school for Chemical Engineering, this is my time to shine!
You got it in the bullet point. A closed system (your container) wants to reach thermal equilibrium. This is done by the warmer item (room temperature water) transferring heat to a place with lower energy (your ice), until thermal equilibrium is achieved.
The thing that actually keeps you container cold isn't the vacuum seal, or at least not entirely. The walls of the container are made of a very good thermal insulator. An insulator prevents your cold water from going through the same thermal equilibrium process with the air temperature, which keeps it cold. It will also work with hot items for the same reason.
The thorough vacuum seal helps prevent heat entry/escape through the seal, but that's not a driving factor.
I'm not entirely sure that you're completely correct about the vacuum not being important. Vacuum flasks are very commonly made primarily of metal, which is conductive. The one I have right next...
The thing that actually keeps you container cold isn't the vacuum seal, or at least not entirely. The walls of the container are made of a very good thermal insulator. An insulator prevents your cold water from going through the same thermal equilibrium process with the air temperature, which keeps it cold. It will also work with hot items for the same reason.
I'm not entirely sure that you're completely correct about the vacuum not being important. Vacuum flasks are very commonly made primarily of metal, which is conductive. The one I have right next to me right now is made of steel. The vacuum doesn't have any media to transmit heat so the only place the heat can go through is the otherwise-insulated lid.
There was some confusion of terminology, so the flask they are describing ('vacuum-sealed') is what the OP stated, not what the OP actually has (vacuum-insulated), and the explanation makes little...
There was some confusion of terminology, so the flask they are describing ('vacuum-sealed') is what the OP stated, not what the OP actually has (vacuum-insulated), and the explanation makes little sense for what the OP has. I'm not actually sure what a vacuum-sealed water bottle would be, or that a vacuum seal would really non-trivially reduce heat entry through the seal compared to a non-vacuum seal in the context of a water bottle.
In any case, the vacuum for a vacuum insulated container is of course of primary importance for the insulation. Shinigami's explanation isn't wrong here in itself, it's just considering the wrong vacuum, and thus the right answer to the wrong question: the thermal insulator is the vacuum between the walls.
Unfortunately, the nature of reddit-like threading systems is such that the answer, which in effect is entirely wrong and misleading for how people will interpret the question, is the first answer most people will see.
So the vacuum is between the inside and outside of the container. If you cut it in half you’d see the outside wall, empty space, and then the inside wall. The top is just a top with a gasket....
So the vacuum is between the inside and outside of the container. If you cut it in half you’d see the outside wall, empty space, and then the inside wall.
The top is just a top with a gasket. Other than that it works like any bottle or glass or fluid container.
The only difference is the vacuum isn’t a good conductor - of hot or cold - and so the contents get to atmospheric temperature much more slowly.
Your intuition is basically correct. Things will tend towards the same temperature if they have a way to exchange energy with each other. In this case, the ice and water can exchange energy with...
Your intuition is basically correct. Things will tend towards the same temperature if they have a way to exchange energy with each other. In this case, the ice and water can exchange energy with each other because they are touching, and so will reach a common temperature if left alone. The warmer thing, the water in this case, has more energy to share. That energy flows from hot to cold, so some of the energy from the water goes into melting the ice. If the water is sufficiently warm, there will be enough energy to completely melt the ice, but unless it is extremely hot, or you have a lot more water than ice, there won't be enough to warm up the melted icewater substantially. So you tend to even out at very cold water, if not water with some ice in it.
Now, the stuff inside the thermos does not have any efficient ways to exchange energy with things outside of the thermos. So it will tend to stay the temperature it is at. This is because it is insulated by a vacuum seal in the walls of the thermos. If there was no vacuum seal, the outside could heat up the wall of the thermos, which touches the contents inside, so they would eventually warm up. If the walls were filled with a layer of air, this would improve things because the outer wall would have to warm up the air, which would then have to warm up the inner wall, which then warms up the contents. Better yet is to evacuate the air from that layer. Now the outside has to warm up the outer wall, which has to radiate its energy to the inner wall, which then warms up the contents. That radiative part is much less efficient than warming up air, so a vacuum between the inner and outer wall really helps to insulate things.
The same principles are at play in how the thermos keeps hot contents hot for so long. You can typically get a good intuition for these things by thinking about how energy is flowing, and in what ways.
You got it right woth equillibrium inside the bottle. The water will melt the ice becomong colder in the process. It will stay at cld temperature for a long time because the heat (or cold as it...
You got it right woth equillibrium inside the bottle. The water will melt the ice becomong colder in the process. It will stay at cld temperature for a long time because the heat (or cold as it works boh ways) in vacuum insulated bottle don't have easy means of escaping (or getting in to the cold water).
Heat can transfer in three ways: conduction, convection or radiation.
Conduction is when you stick mtal rod in fire and it burns yur hand, or if you touch metal rail in winter and feel the cold in your hand.
Convection is actually what hapoens in he bottle when ice is melting - the already colder water sinks to the bottom while still warmer water rises up. The same goes for the air when you light a candle - heat frm the flame rises up thus transfering the heat.
When you insulate water bottle with vacuum (you have bottle in another bottle with a vacuum in between them) there is no way for conduction or convection to happen between water inside it and the outside world. The only way to transfer the heat from or to the inside of the bottle is through radiation which is the worst way to transfer heat from this trio.
It means that the cold water chills the inside bottle while warm air heats the outside bottle. The bottles are not in contact with each other which means the only way of heat getting to cold water is through radiating from outside bottle to inner one. The vacuum between the bottles acts as inulator - be it air, it will get warmer by touching the outsode bottle and transfer heat by conduction.
I have oversimplified there. To get it all clear:
bottles are in contact, they have to be, at the entry point
bottles are made of stainless steel (most of the time) that itself is bot the best heat conductor, this means that the heat has problems going through the part where he bottles are joined - if you on't believe that stainless steel isnpoor conductor, take a spoon and put it in a glass full of hot water and observe the temperature of he handle that sticks out - it won't burn you even though there is hot water just a centimeter away
there has to he some kind of lid on the bottle and it is very likly not vaccum insulated, often made frm plastic, this is the entry way for heat/cold into the bottle - if you pzt hot water in he bottle, the lid will get warm while the rest of the bottle (outside) will keep normal temperature, this cnfirms tha heat escapes through the lid
A few points: Just wanted to clarify to readers of your comment that "cold" is the absence of "heat" and not its own thing. A Thermos does not trap cold in the bottle, per se, it traps heat...
A few points:
Just wanted to clarify to readers of your comment that "cold" is the absence of "heat" and not its own thing. A Thermos does not trap cold in the bottle, per se, it traps heat outside the bottle from warming your cold drink.
You missed an explanation of radiation.
You say steel is a poor heat conductor, but it's not that poor. A metal spoon left in boiling water for a few minutes will be hot enough that it's uncomfortable to handle. Compare that to a plastic or wooden spoon: materials that are far worse at conducting heat. It's actually the cavity between the two the walls of the flask that is providing the bulk of the thermal insulation.
All valid points, thanks for adding them. Nothing to say about cold, you did great! Radiation is basically emitting heat into the space around. It's when you feel the heat from open fire - the...
All valid points, thanks for adding them.
Nothing to say about cold, you did great!
Radiation is basically emitting heat into the space around. It's when you feel the heat from open fire - the heat is radiating from the fire. In the case of vacuum insulated stainless steel water bottles this means that the outer bottle is as warm as room temperature around and it radiates this heat inside through the vacuum to the inside bottle. But radiation being not that efficient energy transfer, it would takelong to warm the cold water, much longer than through other means of transfer. If you had hot waterin the bottle then the inner bottle would radiate the heat towards the outer bottle. (I'm still using the bottle-in-a-bottle thus not speaking about inner and outer wall)
Stainless steel is poor conductor of heat in comparison with some other (often used by people) metals. Basic iron is much better, aluminium is even better than that and copper is great at heat transfer. But stainless steel is great conductor of heat when we compare it to ie. wood, rubber and many other materials. It is the cavity and lack of transfer medium (ie. air) that does the insulation.
If the bottle was made out of copper though, it could transfer the heat through the section where the inner and outter bottles are joined much better than stainless - this was my point that I failed to deliver before.
OK so your flask is effectively creating a closed system for what we're looking at here, meaning that no heat is entering or leaving the system. The water is at or above freezing, 32°F. The ice is...
OK so your flask is effectively creating a closed system for what we're looking at here, meaning that no heat is entering or leaving the system. The water is at or above freezing, 32°F. The ice is at or below freezing. *Heat travels down the thermal gradient, meaning heat goes from hot to cold. So heat will go from the water to the ice, warming up the ice and cooling off the water. Once the ice hits 32°, the heat from the water will start melting the ice instead of warming it until the ice is melted. This continues until all the ice is melted and the water reaches thermal equilibrium. Since our system isn't actually closed, heat will move in (since the inside of the flask is colder than the outside), gradually warming the system until it reaches thermal equilibrium with the surroundings.
I hope this helps, let me know if you have more questions!
*Note that heat is not the same as temperature, it's a sort of measure of energy that temperature tells us about, but two different objects of the same mass at the same temperature will likely have different amounts of heat. Another aspect is that a larger object can hold more heat at the same temperature versus a smaller object of the same material.
An important point here is that melting ice actually takes a large amount of heat. Melting 1 kg of ice, a process which does not change its temperature, takes about four times as much heat as...
An important point here is that melting ice actually takes a large amount of heat. Melting 1 kg of ice, a process which does not change its temperature, takes about four times as much heat as heating 1 kg of water from 0°C to 20°C, ie, from freezing to almost room temperature.
This is why ice is so much more effective at cooling than cold water. It is also why ice only really cools things as it melts: it is the melting itself that is useful for cooling, more than the temperature of the ice.
Addendum: this sort of behavior is well demonstrated by a (simplified) phase chart like the one in the link below, graphing the heat and temperature. You can see how you need to add/remove heat to...
Addendum: this sort of behavior is well demonstrated by a (simplified) phase chart like the one in the link below, graphing the heat and temperature. You can see how you need to add/remove heat to make a phase change happen, phase changes happen at a particular temperature, and how change of temperature only occurs within a given phase.
I just like the diagram, I can't vouch for the rest of the site.
Aside: Some of my favorite posts on Reddit have been the ELI5 posts. One thing I like about them is that, even when I think I know a "simple" concept really well, I still almost invariably learn...
Aside: Some of my favorite posts on Reddit have been the ELI5 posts. One thing I like about them is that, even when I think I know a "simple" concept really well, I still almost invariably learn something new from the ELI5 responses.
I would love to see a tag for a similar theme in Tildes. Do we have one already?
That's pretty much what the ask.experts tag is aiming for. When people want to be able to search/filter for questions that have been answered by people with expertise in their field.
That's pretty much what the ask.experts tag is aiming for. When people want to be able to search/filter for questions that have been answered by people with expertise in their field.
Your understanding is spot on! We can treat a thermos as a closed system. In this context, that means no thermal energy can enter or leave. Thermal energy may sound complicated, but it isn't....
Your understanding is spot on!
We can treat a thermos as a closed system. In this context, that means no thermal energy can enter or leave. Thermal energy may sound complicated, but it isn't. Everything has a specific amount of thermal energy. We can calculate the thermal energy of an item if we know the mass, temperature, and specific heat capacity. The specific heat capacity is a property of a substance. You can think of it as a conversion factor that we use to calculate thermal energy. For example, the specific heat capacity of water is 4.186 J/g°C, and the specific heat capacity of ice is 2.05 J/g°C. Here is some more specific heat capacities
We can calculate the final temperature of the water in the system. Lets say we add 100g water at 80°C to 20g of ice at -10°C. First lets think about the overall system. The ice will absorb energy from the water, and the water will give energy to the ice. Since the thermos is a closed system, the amount of energy absorbed by the ice will equal EXACTLY the energy given by the water (energy cannot be created or destroyed). So all we have to do is calculate how much energy is transferred in the process and we can get the final temperature.
First the ice will move from -10°C to 0°C. The change in temperature is 10°C, and our mass is 20g. Since our specific heat capacity is 2.05 J/g°C, we can use that to calculate the Joules (heat energy) that is consumed. 10 * 20 * 2.05 = 410 J. This energy comes from the water, and we can use that to determine the new temperature: 100g * 4.186 J/g°C * x = 410J. The temperature changes by 0.979455°C. I am going to round it to 1°C. So now we have 100g water at 79°C and 20g ice at 0°C.
Next we have to talk about Enthalpy of Fusion (this has nothing to do with atomic fusion). Water freezes at 0°C, but it still takes energy to change it from a liquid to a solid. You likely understand this intuitively. When you boil a pot of water, all of the water in the pot is at 100°C, and water evaporates at 100°C. But the water doesn't evaporate instantly. You have to keep your stove running for a long time to get the water to evaporate. That is because the water has to absorb energy to convert from a liquid to a gas, even though it doesn't change temperature. The same is true for a solid to a liquid. So the next step in our thermos process is for the ice at 0°C to convert to water at 0°C. The enthalpy of fusion of water is 333.55 J/g. Since we have 20g of ice, it takes 333.55 * 20 = 6671 J to convert our ice into water. Remember, this energy has to come from somewhere, and in our thermos, it has to come from the warm water. So we need to subtract 6671 J from our water: 100g * 4.186 J/g°C * x = 6671 J. Our temperature change at this step is 15.93645 °C (I will round to 16). Our system how has 100g water at 63°C and 20g water at 0°C.
For our last step, we just have to find out what temperature our water will be overall once it reaches equilibrium. This might be slightly more confusing at first, but it is fundamentally exactly the same. Remember that the hot water will give energy and the cold water will receive energy, and the energy that they give and receive is exactly the same. Here is what the equation looks like: 100g * 4.186 J/g°C * ( 63°C - x ) = 20g * 4.186 J/g°C * ( 0°C - x ). We can simplify it to 100(63-x)=20x. Solving for x, we get 52.5. So the final mixture will be 52.5°C.
OP, the other folks around here have done an admirable job of answering the technical questions, so I'm going to focus on something else: your feeling of insecurity or doubt. You asked a good...
OP, the other folks around here have done an admirable job of answering the technical questions, so I'm going to focus on something else: your feeling of insecurity or doubt.
You asked a good question. You had a hypothesis (a prediction based on what you knew), you made an observation (you tested your prediction), and all you lacked was the theory (which explains what you saw in a systematic way, and also makes testable predictions of other phenomena).
You genuinely did science. You took a controlled system that you could not directly observe, and then went about collecting data. You needed help from folks with more training to provide the theory, but so does everyone.
I'm an experimental nuclear chemist, which is a fancy way to say, "I don't know much the theory, but I'm not afraid of radiation or smelly chemicals." I collaborate with theoretical researchers all the time, to help explain what I observed. Sometimes the observations are unexpected or unintuitive, and sometimes the established theories are wrong...and sometimes my observations just suck...but very few people "do it all."
You're in your 40s, and you don't have much science education. There is nothing wrong with that. You do have something unusual and that is worthy of praise: a continuing curiosity and a willingness to ask questions. Embrace that, because it will serve you well!
I'm a professor at a major university, and you would be shocked how many students come in with your same insecurity. I'm talking about top students who have taken multiple advanced science classes before graduating high school, but they all express the same anxiety. Some are afraid to be wrong. Some are afraid to not know. Some are afraid to show that they don't know. All that does is curry doubt in their own mind and gets in the way of their learning. If they would just trust themselves, and trust that they'd learn what they need to learn, they would...I was in their shoes not long ago xD
Be proud of yourself, you've made it to your forties and you're still asking questions. Don't stop unless you want to :)
These vessels require pretreatment for optimum efficiency. Preheat with hottest liquid before adding your beverage. The inverse for cold, except I place mine in the freezer overnight instead of...
These vessels require pretreatment for optimum efficiency. Preheat with hottest liquid before adding your beverage. The inverse for cold, except I place mine in the freezer overnight instead of prechilling with a liquid.
Your question had been answered, but I wondered if I could add a suggestion to the broader audience. It may have been addressed, but might have be buried amongst the answers.
Also, most importantly, please don't feel you need to apologize for your particular circumstances. This is a place to query. No need to justify further.
I went to school for Chemical Engineering, this is my time to shine!
You got it in the bullet point. A closed system (your container) wants to reach thermal equilibrium. This is done by the warmer item (room temperature water) transferring heat to a place with lower energy (your ice), until thermal equilibrium is achieved.
The thing that actually keeps you container cold isn't the vacuum seal, or at least not entirely. The walls of the container are made of a very good thermal insulator. An insulator prevents your cold water from going through the same thermal equilibrium process with the air temperature, which keeps it cold. It will also work with hot items for the same reason.
The thorough vacuum seal helps prevent heat entry/escape through the seal, but that's not a driving factor.
As a slight note here: the bottles the OP is referring to are vacuum-insulated, not (necessarily) vacuum-sealed.
I'm not entirely sure that you're completely correct about the vacuum not being important. Vacuum flasks are very commonly made primarily of metal, which is conductive. The one I have right next to me right now is made of steel. The vacuum doesn't have any media to transmit heat so the only place the heat can go through is the otherwise-insulated lid.
There was some confusion of terminology, so the flask they are describing ('vacuum-sealed') is what the OP stated, not what the OP actually has (vacuum-insulated), and the explanation makes little sense for what the OP has. I'm not actually sure what a vacuum-sealed water bottle would be, or that a vacuum seal would really non-trivially reduce heat entry through the seal compared to a non-vacuum seal in the context of a water bottle.
In any case, the vacuum for a vacuum insulated container is of course of primary importance for the insulation. Shinigami's explanation isn't wrong here in itself, it's just considering the wrong vacuum, and thus the right answer to the wrong question: the thermal insulator is the vacuum between the walls.
Unfortunately, the nature of reddit-like threading systems is such that the answer, which in effect is entirely wrong and misleading for how people will interpret the question, is the first answer most people will see.
So the vacuum is between the inside and outside of the container. If you cut it in half you’d see the outside wall, empty space, and then the inside wall.
The top is just a top with a gasket. Other than that it works like any bottle or glass or fluid container.
The only difference is the vacuum isn’t a good conductor - of hot or cold - and so the contents get to atmospheric temperature much more slowly.
Your intuition is basically correct. Things will tend towards the same temperature if they have a way to exchange energy with each other. In this case, the ice and water can exchange energy with each other because they are touching, and so will reach a common temperature if left alone. The warmer thing, the water in this case, has more energy to share. That energy flows from hot to cold, so some of the energy from the water goes into melting the ice. If the water is sufficiently warm, there will be enough energy to completely melt the ice, but unless it is extremely hot, or you have a lot more water than ice, there won't be enough to warm up the melted icewater substantially. So you tend to even out at very cold water, if not water with some ice in it.
Now, the stuff inside the thermos does not have any efficient ways to exchange energy with things outside of the thermos. So it will tend to stay the temperature it is at. This is because it is insulated by a vacuum seal in the walls of the thermos. If there was no vacuum seal, the outside could heat up the wall of the thermos, which touches the contents inside, so they would eventually warm up. If the walls were filled with a layer of air, this would improve things because the outer wall would have to warm up the air, which would then have to warm up the inner wall, which then warms up the contents. Better yet is to evacuate the air from that layer. Now the outside has to warm up the outer wall, which has to radiate its energy to the inner wall, which then warms up the contents. That radiative part is much less efficient than warming up air, so a vacuum between the inner and outer wall really helps to insulate things.
The same principles are at play in how the thermos keeps hot contents hot for so long. You can typically get a good intuition for these things by thinking about how energy is flowing, and in what ways.
You got it right woth equillibrium inside the bottle. The water will melt the ice becomong colder in the process. It will stay at cld temperature for a long time because the heat (or cold as it works boh ways) in vacuum insulated bottle don't have easy means of escaping (or getting in to the cold water).
Heat can transfer in three ways: conduction, convection or radiation.
Conduction is when you stick mtal rod in fire and it burns yur hand, or if you touch metal rail in winter and feel the cold in your hand.
Convection is actually what hapoens in he bottle when ice is melting - the already colder water sinks to the bottom while still warmer water rises up. The same goes for the air when you light a candle - heat frm the flame rises up thus transfering the heat.
When you insulate water bottle with vacuum (you have bottle in another bottle with a vacuum in between them) there is no way for conduction or convection to happen between water inside it and the outside world. The only way to transfer the heat from or to the inside of the bottle is through radiation which is the worst way to transfer heat from this trio.
It means that the cold water chills the inside bottle while warm air heats the outside bottle. The bottles are not in contact with each other which means the only way of heat getting to cold water is through radiating from outside bottle to inner one. The vacuum between the bottles acts as inulator - be it air, it will get warmer by touching the outsode bottle and transfer heat by conduction.
I have oversimplified there. To get it all clear:
A few points:
All valid points, thanks for adding them.
Nothing to say about cold, you did great!
Radiation is basically emitting heat into the space around. It's when you feel the heat from open fire - the heat is radiating from the fire. In the case of vacuum insulated stainless steel water bottles this means that the outer bottle is as warm as room temperature around and it radiates this heat inside through the vacuum to the inside bottle. But radiation being not that efficient energy transfer, it would takelong to warm the cold water, much longer than through other means of transfer. If you had hot waterin the bottle then the inner bottle would radiate the heat towards the outer bottle. (I'm still using the bottle-in-a-bottle thus not speaking about inner and outer wall)
Stainless steel is poor conductor of heat in comparison with some other (often used by people) metals. Basic iron is much better, aluminium is even better than that and copper is great at heat transfer. But stainless steel is great conductor of heat when we compare it to ie. wood, rubber and many other materials. It is the cavity and lack of transfer medium (ie. air) that does the insulation.
If the bottle was made out of copper though, it could transfer the heat through the section where the inner and outter bottles are joined much better than stainless - this was my point that I failed to deliver before.
OK so your flask is effectively creating a closed system for what we're looking at here, meaning that no heat is entering or leaving the system. The water is at or above freezing, 32°F. The ice is at or below freezing. *Heat travels down the thermal gradient, meaning heat goes from hot to cold. So heat will go from the water to the ice, warming up the ice and cooling off the water. Once the ice hits 32°, the heat from the water will start melting the ice instead of warming it until the ice is melted. This continues until all the ice is melted and the water reaches thermal equilibrium. Since our system isn't actually closed, heat will move in (since the inside of the flask is colder than the outside), gradually warming the system until it reaches thermal equilibrium with the surroundings.
I hope this helps, let me know if you have more questions!
*Note that heat is not the same as temperature, it's a sort of measure of energy that temperature tells us about, but two different objects of the same mass at the same temperature will likely have different amounts of heat. Another aspect is that a larger object can hold more heat at the same temperature versus a smaller object of the same material.
An important point here is that melting ice actually takes a large amount of heat. Melting 1 kg of ice, a process which does not change its temperature, takes about four times as much heat as heating 1 kg of water from 0°C to 20°C, ie, from freezing to almost room temperature.
This is why ice is so much more effective at cooling than cold water. It is also why ice only really cools things as it melts: it is the melting itself that is useful for cooling, more than the temperature of the ice.
Addendum: this sort of behavior is well demonstrated by a (simplified) phase chart like the one in the link below, graphing the heat and temperature. You can see how you need to add/remove heat to make a phase change happen, phase changes happen at a particular temperature, and how change of temperature only occurs within a given phase.
I just like the diagram, I can't vouch for the rest of the site.
https://www.expii.com/t/heating-and-cooling-curves-overview-examples-11108
@IIIIIIIIII, check out the chart too!
Aside: Some of my favorite posts on Reddit have been the ELI5 posts. One thing I like about them is that, even when I think I know a "simple" concept really well, I still almost invariably learn something new from the ELI5 responses.
I would love to see a tag for a similar theme in Tildes. Do we have one already?
That's pretty much what the
ask.expertstag is aiming for. When people want to be able to search/filter for questions that have been answered by people with expertise in their field.Your understanding is spot on!
We can treat a thermos as a closed system. In this context, that means no thermal energy can enter or leave. Thermal energy may sound complicated, but it isn't. Everything has a specific amount of thermal energy. We can calculate the thermal energy of an item if we know the mass, temperature, and specific heat capacity. The specific heat capacity is a property of a substance. You can think of it as a conversion factor that we use to calculate thermal energy. For example, the specific heat capacity of water is 4.186 J/g°C, and the specific heat capacity of ice is 2.05 J/g°C. Here is some more specific heat capacities
We can calculate the final temperature of the water in the system. Lets say we add 100g water at 80°C to 20g of ice at -10°C. First lets think about the overall system. The ice will absorb energy from the water, and the water will give energy to the ice. Since the thermos is a closed system, the amount of energy absorbed by the ice will equal EXACTLY the energy given by the water (energy cannot be created or destroyed). So all we have to do is calculate how much energy is transferred in the process and we can get the final temperature.
First the ice will move from -10°C to 0°C. The change in temperature is 10°C, and our mass is 20g. Since our specific heat capacity is 2.05 J/g°C, we can use that to calculate the Joules (heat energy) that is consumed. 10 * 20 * 2.05 = 410 J. This energy comes from the water, and we can use that to determine the new temperature: 100g * 4.186 J/g°C * x = 410J. The temperature changes by 0.979455°C. I am going to round it to 1°C. So now we have 100g water at 79°C and 20g ice at 0°C.
Next we have to talk about Enthalpy of Fusion (this has nothing to do with atomic fusion). Water freezes at 0°C, but it still takes energy to change it from a liquid to a solid. You likely understand this intuitively. When you boil a pot of water, all of the water in the pot is at 100°C, and water evaporates at 100°C. But the water doesn't evaporate instantly. You have to keep your stove running for a long time to get the water to evaporate. That is because the water has to absorb energy to convert from a liquid to a gas, even though it doesn't change temperature. The same is true for a solid to a liquid. So the next step in our thermos process is for the ice at 0°C to convert to water at 0°C. The enthalpy of fusion of water is 333.55 J/g. Since we have 20g of ice, it takes 333.55 * 20 = 6671 J to convert our ice into water. Remember, this energy has to come from somewhere, and in our thermos, it has to come from the warm water. So we need to subtract 6671 J from our water: 100g * 4.186 J/g°C * x = 6671 J. Our temperature change at this step is 15.93645 °C (I will round to 16). Our system how has 100g water at 63°C and 20g water at 0°C.
For our last step, we just have to find out what temperature our water will be overall once it reaches equilibrium. This might be slightly more confusing at first, but it is fundamentally exactly the same. Remember that the hot water will give energy and the cold water will receive energy, and the energy that they give and receive is exactly the same. Here is what the equation looks like: 100g * 4.186 J/g°C * ( 63°C - x ) = 20g * 4.186 J/g°C * ( 0°C - x ). We can simplify it to 100(63-x)=20x. Solving for x, we get 52.5. So the final mixture will be 52.5°C.
I hope that helps you understand!
OP, the other folks around here have done an admirable job of answering the technical questions, so I'm going to focus on something else: your feeling of insecurity or doubt.
You asked a good question. You had a hypothesis (a prediction based on what you knew), you made an observation (you tested your prediction), and all you lacked was the theory (which explains what you saw in a systematic way, and also makes testable predictions of other phenomena).
You genuinely did science. You took a controlled system that you could not directly observe, and then went about collecting data. You needed help from folks with more training to provide the theory, but so does everyone.
I'm an experimental nuclear chemist, which is a fancy way to say, "I don't know much the theory, but I'm not afraid of radiation or smelly chemicals." I collaborate with theoretical researchers all the time, to help explain what I observed. Sometimes the observations are unexpected or unintuitive, and sometimes the established theories are wrong...and sometimes my observations just suck...but very few people "do it all."
You're in your 40s, and you don't have much science education. There is nothing wrong with that. You do have something unusual and that is worthy of praise: a continuing curiosity and a willingness to ask questions. Embrace that, because it will serve you well!
I'm a professor at a major university, and you would be shocked how many students come in with your same insecurity. I'm talking about top students who have taken multiple advanced science classes before graduating high school, but they all express the same anxiety. Some are afraid to be wrong. Some are afraid to not know. Some are afraid to show that they don't know. All that does is curry doubt in their own mind and gets in the way of their learning. If they would just trust themselves, and trust that they'd learn what they need to learn, they would...I was in their shoes not long ago xD
Be proud of yourself, you've made it to your forties and you're still asking questions. Don't stop unless you want to :)
These vessels require pretreatment for optimum efficiency. Preheat with hottest liquid before adding your beverage. The inverse for cold, except I place mine in the freezer overnight instead of prechilling with a liquid.
Your question had been answered, but I wondered if I could add a suggestion to the broader audience. It may have been addressed, but might have be buried amongst the answers.
Also, most importantly, please don't feel you need to apologize for your particular circumstances. This is a place to query. No need to justify further.