Heat problem (cooler at a beach)

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Homework Help Overview

The discussion revolves around a heat transfer problem involving a cooler at a beach, focusing on the calculation of heat transfer through the cooler's insulation. The participants explore the application of the heat conduction equation and the implications of various parameters such as surface area, temperature difference, and insulation thickness.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the need to calculate the volume of the cooler and the surface area for heat transfer. There are questions about the correct interpretation of variables in the heat transfer equation, particularly regarding the meaning of 'L' and the temperature difference 'ΔT'. Some participants also explore how to incorporate time into the calculations.

Discussion Status

There is an ongoing exploration of the heat transfer equations, with participants providing insights and corrections regarding the parameters involved. Some participants have suggested alternative equations and clarified the definitions of terms, while others are verifying their calculations and assumptions. Multiple interpretations of the problem's dimensions are being considered.

Contextual Notes

Participants note potential ambiguities in the problem statement, particularly regarding whether the dimensions provided refer to the inside or outside of the cooler. This uncertainty influences their calculations and assumptions about the heat transfer process.

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Homework Statement


upload_2015-5-15_1-40-23.png


Homework Equations



Q = kAΔT/L

The Attempt at a Solution


[/B]
so I need to find the volume of the cooler, and then the volume is the volume is ice in it?

then I need to find the surface area of 1 side of the cooler, than multiply it by 6. then plugging in the total area in Q = kAΔT/L

is this a good approach to the problem?
 

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goonking said:

Homework Statement


View attachment 83505

Homework Equations



Q = kAΔT/L (L = latent heat)

The Attempt at a Solution


[/B]
so I need to find the volume of the cooler, and then the volume is the volume is ice in it?

then I need to find the surface area of 1 side of the cooler, than multiply it by 6. then plugging in the total area in Q = kAΔT/L

is this a good approach to the problem?
Hey, that L is not latent heat in equation but length.
 
Raghav Gupta said:
Hey, that L is not latent heat in equation but length.
oh, sorry! good catch
 
goonking said:
oh, sorry! good catch
There is another equation for heat transfer what is that?
 
Raghav Gupta said:
There is another equation for heat transfer what is that?
Q = L m

we equate them so we get

L m = kAΔT/Length

we have L

we have k

we have A and L

I'm assuming ΔT is 29 C?
 
goonking said:
Q = L m

we equate them so we get

L m = kAΔT/Length

we have L

we have k

we have A and L

I'm assuming ΔT is 29 C?
How to bring time term here which is 3 hrs?
 
Raghav Gupta said:
How to bring time term here which is 3 hrs?
i think the answer we get, if we did all the algebra, is the amount of heat per seconds.

so we just convert 3 hours to seconds. then multiply by the heat per seconds

correct?
 
First of all the formula for heat conduction is
Q = kAtΔT/L where k is constant , A is area, t is time, ΔT is temperature difference and L is length.
 
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In case it's not obvious... In this case L is the thickness of the insulation (eg the length of the heat path)
 
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  • #10
Raghav Gupta said:
First of all the formula for heat conduction is
Q = kAtΔT/L where k is constant , A is area, t is time, ΔT is temperature difference and L is length.
Q = (0.035) (0.02m x 0.4m) (10800 seconds) (29 C) / (0.4m) = 219.24 joules

i believe we set Q = L m = 219.24 joules

m should be 6.56x10-4kg

correct?
 
  • #11
goonking said:
Q = (0.035) (0.02m x 0.4m) (10800 seconds) (29 C) / (0.4m) = 219.24 joules

i believe we set Q = L m = 219.24 joules

m should be 6.56x10-4kg

correct?
Yes, it is correct.
 
  • #12
goonking said:
Q = (0.035) (0.02m x 0.4m) (10800 seconds) (29 C) / (0.4m) = 219.24 joules

No "A" is the surface area. You were right when you wrote..

I need to find the surface area of 1 side of the cooler, than multiply it by 6. then plugging in the total area in Q = kAΔT/L

L is the length of the heat path which is through the walls (eg 2cm).
 
  • #13
Yeah, sorry.
The length to be taken is 2cm.
 
  • #14
CWatters said:
No "A" is the surface area. You were right when you wrote..
L is the length of the heat path which is through the walls (eg 2cm).
oh, i forgot to multiply the area by 6, so it should be 6( 0.02m x 0.4m) = A

so new answer should be 26300 joules

i would have never thought the length was 2cm
 
  • #15
goonking said:
i would have never thought the length was 2cm

kAΔT/L gives you the power (energy per second) flowing through the walls. If the walls are thicker (better insulated) then L is longer and less power flows. Make sense?
 
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  • #16
CWatters said:
kAΔT/L gives you the power (energy per second) flowing through the walls. If the walls are thicker (better insulated) then L is longer and less power flows. Make sense?
ok, got the answer to be 1.57 kg, sounds much more reasonable now
 
  • #17
Yes. I make the equation..

Q(Joules) = (0.035) (6 * 0.4m x 0.4m) (10800 seconds) (29 C) / (0.2m)
 
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  • #18
CWatters said:
Yes. I make the equation..

Q(Joules) = (0.035) (6 * 0.4m x 0.4m) (10800 seconds) (29 C) / (0.2m)
should be 0.02 m
 
  • #19
Yes you are right.
 
  • #20
Yes sorry /0.02.
 
  • #21
Raghav Gupta said:
It is 0.157 kg.
make sure you put in 0.02 m, not 0.2m
 
  • #22
Yes, sorry,
Edited.
 
  • #23
Just a thought but..

The question isn't clear if 0.4m is the inside or outside dimension of the box.
 
  • #24
CWatters said:
Just a thought but..

The question isn't clear if 0.4m is the inside or outside dimension of the box.
true, i was thinking that too when I tried to draw out the cooler
 
  • #25
goonking said:
true, i was thinking that too when I tried to draw out the cooler
Isn't the answer given in your problem so you could verify?
 
  • #26
Raghav Gupta said:
Isn't the answer given in your problem so you could verify?
yes, the answer was 1.57 kg
 
  • #27
Ok. Just for info.. If you assume they meant the outside dimension then the insides are about 0.36 * 0.36. If you use that for the area the result is about 1.28kg. Real world the answer will be somewhere in between the two.
 
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