null's math question

[Null]

I have 1mol of iron at 200C, 1mol of copper at 200C, in 100mol of water at 20C. Assume equal distribution of heat in a closed system, don't worry about geometry, assume they interact with each other equally.

What temperature are these elements when they achieve heat equilibrium?
What temperature are each of these substances in 1 second?

 

[{o}P II]

And you took to a cyberbullying website to ask this, why?

 

[Vernerus]

I thought you were moving to Rwanda, but this sounds like the question of someone heading to Greenland.

 

[northstar747]

does jet fuel melt steele?

 

[BarberFerdinand]

Please don't put red hot metal on cold water, it will explode and you might need to go to the hospital.

 

[mr.moon1488]

Unless under extreme pressure, the water will never reach heat equilibrium with the Iron and Copper as it will vaporize.

 

[Ask Jeeves]

Teq = {((mol(Fe)*molecular_mass(Fe)*T(fe)*heat_cap(fe)) + same again copper + same again water)} / {(mol(fe)*molecular_mass(fe)*heat_cap(fe)) + same for copper + same for water)}

units need to be
specific heat capacities in joule/gram
molecular mass in g mol-1
use celcius or kelvin for temperatures

 

[Officer Eradicate]

nigger

 

[Several Goats]

>>>/sci/

 

[BOONES]

Null dont feed the idiots ideas to hurt themselves.

 

[Francesco Dellamorte]

Teq = {((mol(Fe)*molecular_mass(Fe)*T(fe)*heat_cap(fe)) + same again copper + same again water)} / {(mol(fe)*molecular_mass(fe)*heat_cap(fe)) + same for copper + same for water)}

units need to be
specific heat capacities in joule/gram
molecular mass in g mol-1
use celcius or kelvin for temperatures

My DIY method came out to about 31°C. I'd like to see how off I am.
Is this for Breathing Simulator?

 

[Papa Adolfo's Take'n'Bake]

Assumptions:

we are doing a little kiddy version and thus using specific heat capacities defined as 298.15 K, as constants.

The system is isobaric.

Geometry is assumed yo be such that everything just nicely behaves (LMAO)

Iron has a specific heat capacity of 0.45 J*(kg^-1)*(K^-1) , molar weight of 0.055845 (Kg)*(mol^-1)
Tinitial=473.15 K
M=0.055845 kg

Copper has a specific heat Capacity of 0.39 J*(kg^-1)*(K^-1), molar weight of 0.063546 (krxg)*(mol^-1)
Tinitial=473.1
m=0.063546 kg

Water has a specific heat capacity of 4.1379 J*(kg^-1)*(K^-1), molar weight of 0.01801528 (Kg)*(mol^-1)
Tinitial=293.15 K
m=1.801528 kg

Thus we get
(0.45*473.15*0.055845)+(0.39*473.15*0.063546)+(4.1379*293.15*1.801528) = 2,208.9 J fot the total existential heat of the system

Solve the following for 'x' as you assume all substances reach the same temperature.

(0.45*x*0.055845)+(0.39*x*0.063546)+(4.1379*x*1.80152=2,208.9

7.5044*x=2,208.9

x=294.34 K
So, like 21 degrees Centigrade at equilibrium for part one. For part two, you need to take into account that heat capacity also has a time dimension which wasn't relevant to the above calculation I might check back in to maybe do part two but I just finished taking my morning shit and have Church to get ready for.

 

[The Cunting Death]

7

 

[DumbDude42]

What temperature are these elements when they achieve heat equilibrium?

molecular mass of water is 18(1 mol of water is roughly 18 grams)
atomic mass of iron is 56 (1 mol of iron is 56 grams)
copper is 63 (1 mol of copper is 63 grams)
so, in total, you have roughly 1800 grams of water, 56 grams of iron, 63 grams of copper.

that's a large excess of water, and water has a much higher specific heat capacity than those metals, too, so the end result will be a temperature that's only slightly above the initial water temperature. like, 21C or 22C.

What temperature are each of these substances in 1 second?

this can't be answered without knowing the geometry and movements of the system. if your copper/iron are just one solid block of metal then it will take a long time to cool down when dumped in the water, but if it is fine metal powder and you mix it in the water while stirring then you will reach equilibrium very fast.

 

[Un Platano]

Assumptions:

we are doing a little kiddy version and thus using specific heat capacities defined as 278.15 K, as constants.

The system is isobaric.

Geometry is assumed yo be such that everything just nicely behaves (LMAO)

Iron has a specific heat capacity of 0.45 J*(kg^-1)*(K^-1) , molar weight of 0.055845 (Kg)*(mol^-1)
Tinitial=473.15 K
M=0.055845 kg

Copper has a specific heat Capacity of 0.39 J*(kg^-1)*(K^-1), molar weight of 0.063546 (krxg)*(mol^-1)
Tinitial=473.1
m=0.063546 kg

Water has a specific heat capacity of 4.1379 J*(kg^-1)*(K^-1), molar weight of 0.01801528 (Kg)*(mol^-1)
Tinitial=293.15 K
m=1.801528 kg

Thus we get
(0.45*473.15*0.055845)+(0.39*473.15*0.063546)+(4.1379*293.15*1.80152 = 2,208.9 J fot the total existential heat of the system

Solve the following for 'x' as you assume all substances reach the same temperature.

(0.45*x*0.055845)+(0.39*x*0.063546)+(4.1379*x*1.80152=2,208.9

7.5044*x=2,208.9

x=294.34 K
So, like 21 degrees Centigrade at equilibrium for part one. For part two, you need to take into account that heat capacity also has a time dimension which wasn't relevant to the above calculation I might check back in to maybe do part two but I just finished taking my morning shit and have Church to get ready for.

I just solved the temperature and got the same answer, so this checks out.

The second part of the question is not possible to solve without more information. There's two problems with it:
1. The rate of heat transfer between the substances depends on the surface area, and therefore the shape, of the metal. A sphere will lose heat at a lower rate than a cube, which will lose heat at a lower rate than a radiator-shaped piece of metal.
2. The temperature distribution in the substance will not be uniform. The outside of the metal will be at a lower temperature than the center. Temperature could refer to the lowest temperature in the body, or the highest, or the average, or the temperature at some arbitrary point.

Even knowing these things, actually solving the problem is significantly harder than the first. Solving the equilibrium temperature is a high school chemistry problem. Solving the temperature at the second part analytically would stump anyone who hasn't studied graduate level differential equations.

The problem with solving at a certain time is twofold: The first is that the temperature in any given body has multiple methods of heat transfer through the system: Conduction through the body towards its surface, conduction from the body to the water, and convection from the body to the water. Take note that the water is a body just like the iron and copper is, just one that transfers heat through convection as well as conduction. The temperature changing at any one of these points will affect the rate of heat transfer in the other parts of the system. I don't have to attempt to solve this to tell you that this is modelled by a differential equation. Just knowing how these generally go I don't think it's even possible to solve this analytically. You would have to approximate it using numerical methods because the resulting differential equation is not going to be solvable.

The second problem is that there are multiple of these bodies in question. In this case we have three: the iron, the copper, and the water. When the temperature of one changes, this affects the rates of heat transfer in the other two. This is a case of a three body problem (though not one involving gravity, as it usually goes), and again it yields an unsolvable differential equation.

So you have a set of unsolvable differential equations modelling heat transfer nested within an unsolvable differential equation modelling a three body problem. I'm not saying it's impossible to procure an answer from this, but that it will take some truly arcane techniques to do so.

 

[Dilf Department]

Math sucks

 

[Null]

Solving the equilibrium temperature is a high school chemistry problem. Solving the temperature at the second part analytically would stump anyone who hasn't studied graduate level differential equations.

In my simulation I have 'jars' with different matter. They don't necessarily have shape. I was just hoping to do a basic simulation of some physics for the same of complementing gameplay later on.

I just think it'd be really shitty for this to be like, "okay there's now a hot ball in this 3x3 room, so now the ball and the air are all the same temperature immeduately."

What would be a cheap and good enough solution for heat dispersion?

 

[Papa Adolfo's Take'n'Bake]

I just solved the temperature and got the same answer, so this checks out.

The second part of the question is not possible to solve without more information. There's two problems with it:
1. The rate of heat transfer between the substances depends on the surface area, and therefore the shape, of the metal. A sphere will lose heat at a lower rate than a cube, which will lose heat at a slower rate than a radiator-shaped piece of metal.
2. The temperature distribution in the substance will not be uniform. The outside of the metal will be at a lower temperature than the center. Temperature could refer to the lowest temperature in the body, or the highest, or the average, or the temperature at some arbitrary point.

Even knowing these things, actually solving the problem is significantly harder than the first. Solving the equilibrium temperature is a high school chemistry problem. Solving the temperature at the second part analytically would stump anyone who hasn't studied graduate level differential equations.

The problem with solving at a certain time is twofold: The first is that the temperature in any given body has multiple methods of heat transfer through the system: Conduction through the body towards its surface, conduction from the body to the water, and convection from the body to the water. Take note that the water is a body just like the iron and copper is, just one that transfers heat through convection as well as conduction. The temperature changing at any one of these points will affect the rate of heat transfer in the other parts of the system. I don't have to attempt to solve this to tell you that this is modelled by a differential equation. Just knowing how these generally go I don't think it's even possible to solve this analytically. You would have to approximate it using numerical methods because the resulting differential equation is not going to be solvable.

The second problem is that there are multiple of these bodies in question. In this case we have three: the iron, the copper, and the water. When the temperature of one changes, this affects the rates of heat transfer in the other two. This is a case of a three body problem (though not one involving gravity, as it usually goes), and again it yields an unsolvable differential equation.

So you have a set of unsolvable differential equations modelling heat transfer nested within an unsolvable differential equation modelling a three body problem. I'm not saying it's impossible to procure an answer from this, but that it will take some truly arcane techniques to do so.

There is a quick and dirty way to model heat capacity such that you can solve the second part, but it involves dusting off Perry's Chemical Engineering handbook to get the constants and i *might* do it later, but it is somewhat possible for an approximation just using bachelor degree materials and techniques.

 

[DumbDude42]

In my simulation I have 'jars' with different matter. They don't necessarily have shape. I was just hoping to do a basic simulation of some physics for the same of complementing gameplay later on.

I just think it'd be really shitty for this to be like, "okay there's now a hot ball in this 3x3 room, so now the ball and the air are all the same temperature immeduately."

What would be a cheap and good enough solution for heat dispersion?

what is the end goal, what do you need this simulation for? are you trying to make some kind of physics based sandbox game? maybe chemistry lab simulator 2020?

"cheap and good enough solution for heat dispersion" depends a lot on the context and setting you need it for. if you're modeling the behavior of reactants in a reactor vessel you'll want a very high level of detail and accuracy, almost down to the microscopic level. if you're modeling larger scale stuff like temperature change between rooms in a building you'll have to use rough approximations instead because doing detailed low level stuff on that scale is too computationally expensive.

'jars of shapeless matter' sounds very abstract though. maybe just assign one temperature value per jar, and adjust the temperatures of adjacent jars towards the average at a constant rate, and call it a day. but again, i have no idea how detailed or low-level your project is supposed to be so it's hard to make recommendations

 

[Un Platano]

In my simulation I have 'jars' with different matter. They don't necessarily have shape. I was just hoping to do a basic simulation of some physics for the same of complementing gameplay later on.

I just think it'd be really shitty for this to be like, "okay there's now a hot ball in this 3x3 room, so now the ball and the air are all the same temperature immeduately."

What would be a cheap and good enough solution for heat dispersion?

The cheapest and easiest way is using Newton's law of cooling. It's a simple model of cooling between two bodies that assumes that the bodies are a constant temperature throughout, and that the surrounding environment stays constant. This would be an okay approximation since the environment only changes by 1 degree in the given problem. Newton's law of cooling gives a simple exponential equation to model the temperature of a body and it gets close enough without requiring more complex calculations.

There's just one problem with it: Newton's law of cooling requires a heat transfer constant that depends on the exact characteristics of the system like thermal conductivity. This is determined through experimentation. In your case, you'd have to pull a number out of a hat and hope it makes sense.