Make a Thermos: Calculate Final Water Temperature

[Martinez43]

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.

 

[OmCheeto]

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 = T_hot - T_cold)

 

[Martinez43]

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 = T_hot - T_cold)

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.

 

[OmCheeto]

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:

there is still no time in there

Now there is!

(heat transferred)/time = kA(T hot −T cold ) / d​

 

[Martinez43]

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!