Make a Thermos: Calculate Final Water Temperature

In summary, the engineering team is trying to come up with a way to estimate the final temperature of a beaker of water, given the initial temperature and the volume of water. They found an equation on a website that they think will work, but they don't have time to actually solve it. They are looking for help from anyone who may know how to solve for the final temperature.
  • #1
Martinez43
3
1

Homework Statement


Hello,
As part of my engineering orientation class, my team and I have to make a device that can keep a beaker of water warm. We have a list of materials we can and cannot use, but my team and I have decided on aluminum foil and maybe wood. We don't actually have to build this thing, but instead, we have to write a paper on the design and calculations used to determine the final temperature of the water.

The paper is whatever, but what I'm having trouble with is the calculation. The prompt says, "Carry out the necessary calculations to be able to estimate with accuracy the final temperature of the water given the initial condition".

That initial condition is as follows:
(of the water in the beaker)
initial temperature between 60-90 degrees C
initial volume between 50-150 mL (of the water in the beaker)
after a given period of time (anywhere from 20-40 minutes)

Homework Equations


Q=mcΔT
Q= KA(T hot −T cold ) / d[/B]

The Attempt at a Solution


I spent some time googling equations and concepts. First I was thinking r-values, like in insulation, but I turned away from that rather quickly. In the prompt paper, they talk about Thermal Conductivity, which was how I found that the second equation.

My last idea was to solve for thermal conductivity for each of my materials, set that equal to mcΔT of water, I could solve for mass with the density of water, and I would get my final temperature. Hopefully, that made sense. But, number one, I don't think I can set those two equal, and, number two, there is still no time in there.

No one else on my team has really proposed anything else as we, and most of the class are a bit confused, to say the least. We are freshmen, by the way, we know some physics and chemistry, but nothing too crazy

So, if anyone has any suggestions, ideas, formulas, I would highly appreciate it.
 
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  • #2
Martinez43 said:
Q= KA(T hot −T cold ) / d
Where did you find this equation?
A similar equation I found at Wikipedia under "Thermal Insulation" has it written as: "something other than Q" = kA∆T/d
(where ∆T = Thot - Tcold)
 
  • #3
OmCheeto said:
Where did you find this equation?
A similar equation I found at Wikipedia under "Thermal Insulation" has it written as: "something other than Q" = kA∆T/d
(where ∆T = Thot - Tcold)

https://thermtest.com/thermal-resources/conduction-calculator

It says Q, but then I realized they're not really the same thing and that is where my idea went through the window.
 
  • #4
Martinez43 said:
https://thermtest.com/thermal-resources/conduction-calculator

It says Q, but then I realized they're not really the same thing and that is where my idea went through the window.
Very annoying. Someone should send that website an email.

From that website: "Q = Conduction heat transfer (W)"
"W" standing for "watts"

Wikipedia uses the symbol "P" for power, also in watts.

I'm not sure which branch of science uses "Q" for "power". hmmmm... Anyways...

At the Khan Academy, they express the equation as Q/t = kA∆T/d
which is much more to my liking, as you mentioned:
Martinez43 said:
there is still no time in there
Now there is!
(heat transferred)/time = kA(T hot −T cold ) / d​
 
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  • #5
I had literally just watched that video but forgot! Thanks for reminding me lol. Ok so,
Find the new Q of each material, add them up, that over time is equal to mcΔT of water, solve for T final.
That sounds a lot better to me!
 

1. How does a thermos work?

A thermos works by using a vacuum seal to trap heat and prevent it from escaping. The inner and outer walls of the thermos are made of materials that are poor conductors of heat, such as glass or plastic, which further helps to keep the contents at a constant temperature.

2. What factors affect the final water temperature in a thermos?

The final water temperature in a thermos is affected by several factors, including the initial temperature of the water, the volume of water, the material and thickness of the thermos walls, and the ambient temperature of the surroundings. These factors can all impact the rate at which heat is lost from the water.

3. How do I calculate the final water temperature in a thermos?

The final water temperature in a thermos can be calculated using the following formula: Tfinal = (Tinitial * Vinitial + Tambient * Vambient) / (Vinitial + Vambient), where Tfinal is the final water temperature, Tinitial is the initial water temperature, Vinitial is the initial volume of water, Tambient is the ambient temperature, and Vambient is the volume of air in the thermos.

4. Does the shape of a thermos affect its ability to retain heat?

Yes, the shape of a thermos can affect its ability to retain heat. A tall, narrow thermos will have a smaller surface area and thus less heat loss compared to a short, wide thermos with a larger surface area. However, the material and thickness of the thermos walls also play a significant role in heat retention.

5. How can I improve the heat retention of my thermos?

To improve the heat retention of your thermos, you can try preheating the thermos with hot water before adding your desired liquid. You can also use a thermos with thicker walls or made of materials with better insulating properties, such as stainless steel. Closing the thermos tightly and avoiding frequent opening can also help to retain heat for longer periods.

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